document_title: United States dollar

question_text: what is on the back of 2 dollar bill

question_tokens: what is on the back of 2 dollar bill

text: United States dollar

text: Overview[edit]

text: Article I, Section 8 of the U.S. Constitution provides that the Congress has the power "To coin money".[13] Laws implementing this power are currently codified at 31 U.S.C. § 5112. Section 5112 prescribes the forms in which the United States dollars should be issued.[14] These coins are both designated in Section 5112 as "legal tender" in payment of debts.[14] The Sacagawea dollar is one example of the copper alloy dollar. The pure silver dollar is known as the American Silver Eagle. Section 5112 also provides for the minting and issuance of other coins, which have values ranging from one cent to 100 dollars.[14] These other coins are more fully described in Coins of the United States dollar.

text: The Constitution provides that "a regular Statement and Account of the Receipts and Expenditures of all public Money shall be published from time to time".[15] That provision of the Constitution is made specific by Section 331 of Title 31 of the United States Code.[16] The sums of money reported in the "Statements" are currently being expressed in U.S. dollars (for example, see the 2009 Financial Report of the United States Government).[17] The U.S. dollar may therefore be described as the unit of account of the United States.

text: The word "dollar" is one of the words in the first paragraph of Section 9 of Article I of the Constitution. There, "dollars" is a reference to the Spanish milled dollar, a coin that had a monetary value of 8 Spanish units of currency, or reales. In 1792 the U.S. Congress passed a Coinage Act. Section 9 of that act authorized the production of various coins, including "DOLLARS OR UNITS—each to be of the value of a Spanish milled dollar as the same is now current, and to contain three hundred and seventy-one grains and four sixteenth parts of a grain of pure, or four hundred and sixteen grains of standard silver". Section 20 of the act provided, "That the money of account of the United States shall be expressed in dollars, or units... and that all accounts in the public offices and all proceedings in the courts of the United States shall be kept and had in conformity to this regulation". In other words, this act designated the United States dollar as the unit of currency of the United States.

text: Unlike the Spanish milled dollar, the U.S. dollar is based upon a decimal system of values. In addition to the dollar the coinage act officially established monetary units of mill or one-thousandth of a dollar (symbol ₥), cent or one-hundredth of a dollar (symbol ¢), dime or one-tenth of a dollar, and eagle or ten dollars, with prescribed weights and composition of gold, silver, or copper for each. It was proposed in the mid-1800s that one hundred dollars be known as a union, but no union coins were ever struck and only patterns for the $50 half union exist. However, only cents are in everyday use as divisions of the dollar; "dime" is used solely as the name of the coin with the value of 10¢, while "eagle" and "mill" are largely unknown to the general public, though mills are sometimes used in matters of tax levies, and gasoline prices are usually in the form of $X.XX9 per gallon, e.g., $3.599, more commonly written as $3.599⁄10. When currently issued in circulating form, denominations equal to or less than a dollar are emitted as U.S. coins while denominations equal to or greater than a dollar are emitted as Federal Reserve notes (with the exception of gold, silver and platinum coins valued up to $100 as legal tender, but worth far more as bullion). Both one-dollar coins and notes are produced today, although the note form is significantly more common. In the past, "paper money" was occasionally issued in denominations less than a dollar (fractional currency) and gold coins were issued for circulation up to the value of $20 (known as the "double eagle", discontinued in the 1930s). The term eagle was used in the Coinage Act of 1792 for the denomination of ten dollars, and subsequently was used in naming gold coins. Paper currency less than one dollar in denomination, known as "fractional currency", was also sometimes pejoratively referred to as "shinplasters". In 1854, James Guthrie, then Secretary of the Treasury, proposed creating $100, $50 and $25 gold coins, which were referred to as a "Union", "Half Union", and "Quarter Union",[18] thus implying a denomination of 1 Union = $100.

text: Today, USD notes are made from cotton fiber paper, unlike most common paper, which is made of wood fiber. U.S. coins are produced by the United States Mint. U.S. dollar banknotes are printed by the Bureau of Engraving and Printing and, since 1914, have been issued by the Federal Reserve. The "large-sized notes" issued before 1928 measured 7.42 by 3.125 inches (188.5 by 79.4 mm); small-sized notes, introduced that year, measure 6.14 by 2.61 by 0.0043 inches (155.96 by 66.29 by 0.11 mm). When the current, smaller sized U.S. currency was introduced it was referred to as Philippine-sized currency because the Philippines had previously adopted the same size for its legal currency.

text: Etymology[edit]

text: In the 16th century, Count Hieronymus Schlick of Bohemia began minting coins known as Joachimstalers (from German thal, or nowadays usually Tal, "valley", cognate with "dale" in English), named for Joachimstal, the valley where the silver was mined (St. Joachim's Valley, now Jáchymov; then part of the Kingdom of Bohemia, now part of the Czech Republic).[19] Joachimstaler was later shortened to the German Taler, a word that eventually found its way into Danish and Swedish as daler, Norwegian as dalar and daler, Dutch as daler or daalder, Ethiopian as ታላሪ (talari), Hungarian as tallér, Italian as tallero, and English as dollar.[19] Alternatively, thaler is said to come from the German coin Guldengroschen ("great guilder", being of silver but equal in value to a gold guilder), minted from the silver from Joachimsthal.

text: The coins minted at Joachimsthal soon lent their name to other coins of similar size and weight from other places. One such example, was a Dutch coin depicting a lion, hence its Dutch name leeuwendaler (in English: lion dollar).

text: The leeuwendaler was authorized to contain 427.16 grains of .75 fine silver and passed locally for between 36 and 42 stuivers. It was lighter than the large-denomination coins then in circulation, thus it was more advantageous for a Dutch merchant to pay a foreign debt in leeuwendalers and it became the coin of choice for foreign trade.

text: The leeuwendaler was popular in the Dutch East Indies and in the Dutch New Netherland Colony (New York), and circulated throughout the Thirteen Colonies during the 17th and early 18th centuries. It was also popular throughout Eastern Europe, where it led to the current Romanian and Moldovan currency being called leu (literally "lion").

text: Among the English-speaking community, the coin came to be popularly known as lion dollar – and is the origin of the name dollar.[20] The modern American-English pronunciation of dollar is still remarkably close to the 17th-century Dutch pronunciation of daler.[21]

text: By analogy with this lion dollar, Spanish pesos – with the same weight and shape as the lion dollar – came to be known as Spanish dollars.[21] By the mid-18th century, the lion dollar had been replaced by the Spanish dollar, the famous "piece of eight", which was distributed widely in the Spanish colonies in the New World and in the Philippines.[22] Eventually, dollar became the name of the first official American currency.

text: Nicknames[edit]

text: The colloquialism "buck"(s) (much like the British word "quid"(s, pl) for the pound sterling) is often used to refer to dollars of various nations, including the U.S. dollar. This term, dating to the 18th century, may have originated with the colonial leather trade. It may also have originated from a poker term.[23] "Greenback" is another nickname originally applied specifically to the 19th century Demand Note dollars created by Abraham Lincoln to finance the costs of the Civil War for the North.[24] The original note was printed in black and green on the back side. It is still used to refer to the U.S. dollar (but not to the dollars of other countries). Other well-known names of the dollar as a whole in denominations include "greenmail", "green" and "dead presidents" (the last because deceased presidents are pictured on most bills).

text: A "grand", sometimes shortened to simply "G", is a common term for the amount of $1,000. The suffix "K" or "k" (from "kilo-") is also commonly used to denote this amount (such as "$10k" to mean $10,000). However, the $1,000 note is no longer in general use. A "large" or "stack", it is usually a reference to a multiple of $1,000 (such as "fifty large" meaning $50,000). The $100 note is nicknamed "Benjamin", "Benji", "Ben", or "Franklin" (after Benjamin Franklin), "C-note" (C being the Roman numeral for 100), "Century note" or "bill" (e.g. "two bills" being $200). The $50 note is occasionally called a "yardstick" or a "grant" (after President Ulysses S. Grant, pictured on the obverse). The $20 note is referred to as a "double sawbuck", "Jackson" (after Andrew Jackson), or "double eagle". The $10 note is referred to as a "sawbuck", "ten-spot" or "Hamilton" (after Alexander Hamilton). The $5 note as "Lincoln", "fin", "fiver" or "five-spot". The infrequently-used $2 note is sometimes called "deuce", "Tom", or "Jefferson" (after Thomas Jefferson). The $1 note as a "single" or "buck". The dollar has also been referred to as a "bone" and "bones" in plural (e.g. "twenty bones" is equal to $20). The newer designs, with portraits displayed in the main body of the obverse (rather than in cameo insets), upon paper color-coded by denomination, are sometimes referred to as "bigface" notes or "Monopoly money".

text: "Piastre" was the original French word for the U.S. dollar, used for example in the French text of the Louisiana Purchase. Calling the dollar a piastre is still common among the speakers of Cajun French and New England French. Modern French uses dollar for this unit of currency as well. The term is still used as slang for U.S. dollars in the French-speaking Caribbean islands, most notably Haiti.

text: Dollar sign[edit]

text: The symbol $, usually written before the numerical amount, is used for the U.S. dollar (as well as for many other currencies). The sign was the result of a late 18th-century evolution of the scribal abbreviation "ps" for the peso, the common name for the Spanish dollars that were in wide circulation in the New World from the 16th to the 19th centuries. These Spanish pesos or dollars were minted in Spanish America, namely in Mexico City; Potosí, Bolivia; and Lima, Peru. The p and the s eventually came to be written over each other giving rise to $.[25][26][27][28]

text: Another popular explanation is that it is derived from the Pillars of Hercules on the Spanish Coat of arms of the Spanish dollar. These Pillars of Hercules on the silver Spanish dollar coins take the form of two vertical bars (||) and a swinging cloth band in the shape of an "S".

text: Yet another explanation suggests that the dollar sign was formed from the capital letters U and S written or printed one on top of the other. This theory, popularized by novelist Ayn Rand in Atlas Shrugged,[29] does not consider the fact that the symbol was already in use before the formation of the United States.[30]

text: History[edit]

text: The American dollar coin was initially based on the value and look of the Spanish dollar, used widely in Spanish America from the 16th to the 19th centuries. The first dollar coins issued by the United States Mint (founded 1792) were similar in size and composition to the Spanish dollar, minted in Mexico and Peru. The Spanish, U.S. silver dollars, and later, Mexican silver pesos circulated side by side in the United States, and the Spanish dollar and Mexican peso remained legal tender until the Coinage Act of 1857. The coinage of various English colonies also circulated. The lion dollar was popular in the Dutch New Netherland Colony (New York), but the lion dollar also circulated throughout the English colonies during the 17th century and early 18th century. Examples circulating in the colonies were usually worn so that the design was not fully distinguishable, thus they were sometimes referred to as "dog dollars".[31]

text: The U.S. dollar was first defined by the Coinage Act of 1792, which specified a "dollar" to be based in the Spanish milled dollar and of 371 grains and 4 sixteenths part of a grain of pure or 416 grains (27.0 g) of standard silver and an "eagle" to be 247 and 4 eighths of a grain or 270 grains (17 g) of gold (again depending on purity).[32] The choice of the value 371 grains arose from Alexander Hamilton's decision to base the new American unit on the average weight of a selection of worn Spanish dollars. Hamilton got the treasury to weigh a sample of Spanish dollars and the average weight came out to be 371 grains. A new Spanish dollar was usually about 377 grains in weight, and so the new U.S. dollar was at a slight discount in relation to the Spanish dollar.

text: The same coinage act also set the value of an eagle at 10 dollars, and the dollar at 1⁄10 eagle. It called for 90% silver alloy coins in denominations of 1, 1⁄2, 1⁄4, 1⁄10, and 1⁄20 dollars; it called for 90% gold alloy coins in denominations of 1, 1⁄2, 1⁄4, and 1⁄10 eagles. The value of gold or silver contained in the dollar was then converted into relative value in the economy for the buying and selling of goods. This allowed the value of things to remain fairly constant over time, except for the influx and outflux of gold and silver in the nation's economy.[33]

text: The early currency of the United States did not exhibit faces of presidents, as is the custom now;[34] although today, by law, only the portrait of a deceased individual may appear on United States currency.[35] In fact, the newly formed government was against having portraits of leaders on the currency, a practice compared to the policies of European monarchs.[36] The currency as we know it today did not get the faces they currently have until after the early 20th century; before that "heads" side of coinage used profile faces and striding, seated, and standing figures from Greek and Roman mythology and composite Native Americans. The last coins to be converted to profiles of historic Americans were the dime (1946) and the Dollar (1971).

text: For articles on the currencies of the colonies and states, see Connecticut pound, Delaware pound, Georgia pound, Maryland pound, Massachusetts pound, New Hampshire pound, New Jersey pound, New York pound, North Carolina pound, Pennsylvania pound, Rhode Island pound, South Carolina pound, and Virginia pound.

text: Continental currency[edit]

text: During the American Revolution the thirteen colonies became independent states. Freed from British monetary regulations, they each issued £sd paper money to pay for military expenses. The Continental Congress also began issuing "Continental Currency" denominated in Spanish dollars. The dollar was valued relative to the states' currencies at the following rates:

text:
5 shillings – Georgia
6 shillings – Connecticut, Massachusetts, New Hampshire, Rhode Island, Virginia
7 1⁄2 shillings – Delaware, Maryland, New Jersey, Pennsylvania
8 shillings – New York, North Carolina
32 1⁄2 shillings – South Carolina

tag: ul

text: Continental currency depreciated badly during the war, giving rise to the famous phrase "not worth a continental".[37] A primary problem was that monetary policy was not coordinated between Congress and the states, which continued to issue bills of credit. Additionally, neither Congress nor the governments of the several states had the will or the means to retire the bills from circulation through taxation or the sale of bonds.[38] The currency was ultimately replaced by the silver dollar at the rate of 1 silver dollar to 1000 continental dollars.

text: Silver and gold standards[edit]

text: From 1792, when the Mint Act was passed, the dollar was defined as 371.25 grains (24.056 g) of silver. The gold coins that were minted were not given any denomination and traded for a market value relative to the Congressional standard of the silver dollar. 1834 saw a shift in the gold standard to 23.2 grains (1.50 g), followed by a slight adjustment to 23.22 grains (1.505 g) in 1837 (16:1 ratio).[citation needed]

text: In 1862, paper money was issued without the backing of precious metals, due to the Civil War. Silver and gold coins continued to be issued and in 1878 the link between paper money and coins was reinstated. This disconnection from gold and silver backing also occurred during the War of 1812. The use of paper money not backed by precious metals had also occurred under the Articles of Confederation from 1777 to 1788. With no solid backing and being easily counterfeited, the continentals quickly lost their value, giving rise to the phrase "not worth a continental". This was a primary reason for the "No state shall... make any thing but gold and silver coin a tender in payment of debts" clause in article 1, section 10 of the United States Constitution.

text: In order to finance the War of 1812, Congress authorized the issuance of Treasury Notes, interest-bearing short-term debt that could be used to pay public dues. While they were intended to serve as debt, they did function "to a limited extent" as money. Treasury Notes were again printed to help resolve the reduction in public revenues resulting from the Panic of 1837 and the Panic of 1857, as well as to help finance the Mexican–American War and the Civil War.

text: In addition to Treasury Notes, in 1861, Congress authorized the Treasury to borrow $50 million in the form of Demand Notes, which did not bear interest but could be redeemed on demand for precious metals. However, by December 1861, the Union government's supply of specie was outstripped by demand for redemption and they were forced to suspend redemption temporarily. The following February, Congress passed the Legal Tender Act of 1862, issuing United States Notes, which were not redeemable on demand and bore no interest, but were legal tender, meaning that creditors had to accept them at face value for any payment except for public debts and import tariffs. However, silver and gold coins continued to be issued, resulting in the depreciation of the newly printed notes through Gresham's Law. In 1869, Supreme Court ruled in Hepburn v. Griswold that Congress could not require creditors to accept United States Notes, but overturned that ruling the next year in the Legal Tender Cases. In 1875, Congress passed the Specie Payment Resumption Act, requiring the Treasury to allow US Notes to be redeemed for gold after January 1, 1879. The Treasury ceased to issue United States Notes in 1971.

text: The Gold Standard Act of 1900 abandoned the bimetallic standard and defined the dollar as 23.22 grains (1.505 g) of gold, equivalent to setting the price of 1 troy ounce of gold at $20.67. Silver coins continued to be issued for circulation until 1964, when all silver was removed from dimes and quarters, and the half dollar was reduced to 40% silver. Silver half dollars were last issued for circulation in 1970. Gold coins were confiscated by Executive Order 6102 issued in 1933 by Franklin Roosevelt. The gold standard was changed to 13.71 grains (0.888 g), equivalent to setting the price of 1 troy ounce of gold at $35. This standard persisted until 1968.

text: Between 1968 and 1975, a variety of pegs to gold were put in place, eventually culminating in a sudden end, on August 15, 1971, to the convertibility of dollars to gold later dubbed the Nixon Shock. The last peg was $42.22 per ounce[citation needed] before the U.S. dollar was allowed to freely float on currency markets.

text: According to the Bureau of Engraving and Printing, the largest note it ever printed was the $100,000 Gold Certificate, Series 1934. These notes were printed from December 18, 1934, through January 9, 1935, and were issued by the Treasurer of the United States to Federal Reserve Banks only against an equal amount of gold bullion held by the Treasury. These notes were used for transactions between Federal Reserve Banks and were not circulated among the general public.

text: Coins[edit]

text: Official United States coins have been produced every year from 1792 to the present.

text:
Denomination
Common name
Front
Reverse
Portrait and design date
Reverse motif and design date
Weight
Diameter
Material
Edge
Circulation

Cent
1¢
penny

Abraham Lincoln
Union Shield
2.5 g
(0.088 oz)
0.75 in
(19.05 mm)
97.5% Zn
2.5% Cu
plain
Wide

Five-Cent
5¢
nickel

Thomas Jefferson
Monticello
5 g
(0.176 oz)
0.835 in
(21.21 mm)
75% Cu
25% Ni
plain
Wide

Dime
10¢
dime

Franklin D. Roosevelt
olive branch, torch, oak branch
0.08 oz
(2.268 g)
0.705 in
(17.91 mm)
91.67% Cu
8.33% Ni
118 reeds
Wide

Quarter Dollar
25¢
quarter

George Washington
Various; five designs per year
0.2 oz
(5.67 g)
0.955 in
(24.26 mm)
91.67% Cu
8.33% Ni
119 reeds
Wide

Half Dollar
50¢
half

John F. Kennedy
Presidential Seal
0.4 oz
(11.34 g)
1.205 in
(30.61 mm)
91.67% Cu
8.33% Ni
150 reeds
Limited

Dollar coin
$1
dollar coin, golden dollar

Profile of Sacagawea with her child, Jean Baptiste Charbonneau
Bald eagle in flight (2000–2008), Various; new design per year
0.286 oz
(8.10 g)
1.043 in
(26.50 mm)
88.5% Cu
6% Zn
3.5% Mn
2% Ni
Lettered
Limited

text: Discontinued coin denominations include:

text:
Half cent: 1⁄2¢, 1793–1857
Fugio Cent: 1¢, 1787
Two-cent piece: 2¢, 1863–1873
Three-cent bronze: 3¢, 1863 (not circulated)
Three-cent nickel: 3¢, 1865–1889
Trime: 3¢, 1851–1873
Half dime: 5¢, 1792–1873
Twenty-cent piece: 20¢, 1875–1878
Gold dollar: $1.00, 1849–1889
Quarter eagle: $2.50, 1792–1929
Three-dollar piece: $3.00, 1854–1889
Stella: $4.00, (not circulated)
Half eagle: $5.00, 1795–1929, minted as a commemorative 1986–present
Eagle: $10.00, minted as a commemorative 1984–2003
Double eagle: $20.00, 1849–1933, 2009
Half-union: $50.00, 1877 (pattern only), 1915 (Panama–Pacific International Exposition coin)
Union: $100.00, 2015 (High relief; not circulated)

text: Collector coins for which everyday transactions are non-existent.[39]

text:
American Eagles originally were not available from the Mint for individuals but had to be purchased from authorized dealers. In 2006 The Mint began direct sales to individuals of uncirculated bullion coins with a special finish, and bearing a "W" mintmark.

American Silver Eagle $1 (1 troy ounce) silver bullion coin 1986–present
American Gold Eagle $5 (1⁄10 troy oz), $10 (1⁄4 troy oz), $25 (1⁄2 troy oz), and $50 (1 troy oz) Gold bullion coin 1986–present
American Platinum Eagle ($10, $25, $50, and $100 platinum coin) 1997–present

United States commemorative coins—special issue coins

$50.00 (Half Union) 1915
Presidential Proofs (see below) 2007–present

text: Technically, all these coins are still legal tender at face value, though some are far more valuable today for their numismatic value, and for gold and silver coins, their precious metal value. From 1965 to 1970 the Kennedy half dollar was the only circulating coin with any silver content, which was removed in 1971 and replaced with cupronickel. However, since 1992, the U.S. Mint has produced special Silver Proof Sets in addition to the regular yearly proof sets with silver dimes, quarters, and half dollars in place of the standard copper-nickel versions. In addition, an experimental $4.00 (Stella) coin was also minted in 1879, but never placed into circulation, and is properly considered to be a pattern rather than an actual coin denomination.

text: The $50 coin mentioned was only produced in 1915 for the Panama-Pacific International Exposition (1915) celebrating the opening of the Panama Canal. Only 1,128 were made, 645 of which were octagonal; this remains the only U.S. coin that was not round as well as the largest and heaviest U.S. coin ever produced.

text: A $100 gold coin was produced in High relief during 2015, although it was primarily produced for collectors, not for general circulation.[40]

text: From 1934 to present, the only denominations produced for circulation have been the familiar penny, nickel, dime, quarter, half dollar and dollar. The nickel is the only coin still in use today that is essentially unchanged (except in its design) from its original version. Every year since 1866, the nickel has been 75% copper and 25% nickel, except for 4 years during World War II when nickel was needed for the war.

text: Due to the penny's low value, some efforts have been made to eliminate the penny as circulating coinage.[41][42]

text: Collector coins[edit]

text: The United States Mint produces Proof Sets specifically for collectors and speculators. Silver Proofs tend to be the standard designs but with the dime, quarter, and half dollar containing 90% silver. Starting in 1983 and ending in 1997, the Mint also produced proof sets containing the year's commemorative coins alongside the regular coins. Another type of proof set is the Presidential Dollar Proof Set where four special $1 coins are minted each year featuring a president. Because of budget constraints and increasing stockpiles of these relatively unpopular coins, the production of new Presidential dollar coins for circulation was suspended on December 13, 2011, by U.S. Treasury Secretary Timothy F. Geithner. Future minting of such coins will be made solely for collectors.[43]

text:
2007 had George Washington, John Adams, Thomas Jefferson, and James Madison
2008 had James Monroe, John Quincy Adams, Andrew Jackson, and Martin Van Buren
2009 had William Henry Harrison, John Tyler, James K. Polk, and Zachary Taylor
2010 had Millard Fillmore, Franklin Pierce, James Buchanan, and Abraham Lincoln
2011 had Andrew Johnson, Ulysses S. Grant, Rutherford B. Hayes, and James A. Garfield
2012 had Chester Arthur, Grover Cleveland (1st term), Benjamin Harrison, and Grover Cleveland (2nd term)
2013 had William McKinley, Theodore Roosevelt, William Howard Taft and Woodrow Wilson
2014 had Warren G. Harding, Calvin Coolidge, Herbert Hoover, and Franklin D. Roosevelt
2015 had Harry S Truman, Dwight D. Eisenhower, John F. Kennedy, and Lyndon B. Johnson
2016 had Richard M. Nixon, Gerald R. Ford and Ronald Reagan.

text: Dollar coins[edit]

text: The first United States dollar was minted in 1794. Known as the Flowing Hair Dollar, contained 416 grains of "standard silver" (89.25% silver and 10.75% copper), as specified by Section 13[44] of the Coinage Act of 1792. It was designated by Section 9 of that Act as having "the value of a Spanish milled dollar".

text: Dollar coins have not been very popular in the United States.[45] Silver dollars were minted intermittently from 1794 through 1935; a copper-nickel dollar of the same large size, featuring President Dwight D. Eisenhower, was minted from 1971 through 1978. Gold dollars were also minted in the 19th century. The Susan B. Anthony dollar coin was introduced in 1979; these proved to be unpopular because they were often mistaken for quarters, due to their nearly equal size, their milled edge, and their similar color. Minting of these dollars for circulation was suspended in 1980 (collectors' pieces were struck in 1981), but, as with all past U.S. coins, they remain legal tender. As the number of Anthony dollars held by the Federal Reserve and dispensed primarily to make change in postal and transit vending machines had been virtually exhausted, additional Anthony dollars were struck in 1999. In 2000, a new $1 coin, featuring Sacagawea, (the Sacagawea dollar) was introduced, which corrected some of the problems of the Anthony dollar by having a smooth edge and a gold color, without requiring changes to vending machines that accept the Anthony dollar. However, this new coin has failed to achieve the popularity of the still-existing $1 bill and is rarely used in daily transactions. The failure to simultaneously withdraw the dollar bill and weak publicity efforts have been cited by coin proponents as primary reasons for the failure of the dollar coin to gain popular support.[46]

text: In February 2007, the U.S. Mint, under the Presidential $1 Coin Act of 2005,[47] introduced a new $1 U.S. Presidential dollar coin. Based on the success of the "50 State Quarters" series, the new coin features a sequence of presidents in order of their inaugurations, starting with George Washington, on the obverse side. The reverse side features the Statue of Liberty. To allow for larger, more detailed portraits, the traditional inscriptions of "E Pluribus Unum", "In God We Trust", the year of minting or issuance, and the mint mark will be inscribed on the edge of the coin instead of the face. This feature, similar to the edge inscriptions seen on the British £1 coin, is not usually associated with U.S. coin designs. The inscription "Liberty" has been eliminated, with the Statue of Liberty serving as a sufficient replacement. In addition, due to the nature of U.S. coins, this will be the first time there will be circulating U.S. coins of different denominations with the same president featured on the obverse (heads) side (Lincoln/penny, Jefferson/nickel, Franklin D. Roosevelt/dime, Washington/quarter, Kennedy/half dollar, and Eisenhower/dollar). Another unusual fact about the new $1 coin is Grover Cleveland will have two coins with two different portraits issued due to the fact he was the only U.S. President to be elected to two non-consecutive terms.[48]

text: Early releases of the Washington coin included error coins shipped primarily from the Philadelphia mint to Florida and Tennessee banks. Highly sought after by collectors, and trading for as much as $850 each within a week of discovery, the error coins were identified by the absence of the edge impressions "E PLURIBUS UNUM IN GOD WE TRUST 2007 P". The mint of origin is generally accepted to be mostly Philadelphia, although identifying the source mint is impossible without opening a mint pack also containing marked units. Edge lettering is minted in both orientations with respect to "heads", some amateur collectors were initially duped into buying "upside down lettering error" coins.[49] Some cynics also erroneously point out that the Federal Reserve makes more profit from dollar bills than dollar coins because they wear out in a few years, whereas coins are more permanent. The fallacy of this argument arises because new notes printed to replace worn out notes, which have been withdrawn from circulation, bring in no net revenue to the government to offset the costs of printing new notes and destroying the old ones. As most vending machines are incapable of making change in banknotes, they commonly accept only $1 bills, though a few will give change in dollar coins.

text: Mint marks[edit]

text:
Mint
Mint mark
Metal minted
Year established
Current status

Denver
D
All metals
1906
Facility open

Philadelphia
P or none[a]
All metals
1792
Facility open

San Francisco
S
All metals
1854
Facility open (proof only)

West Point
W or none[b]
Gold, Silver and Platinum
1973
Facility open (bullion only)

Carson City
CC
Gold and Silver
1870
Facility closed, 1893[c]

Charlotte
C
Gold only
1838
Facility closed, 1861

Dahlonega
D[d]
Gold only
1838
Facility closed, 1861

Manila[e]
M or none[f]
All metals
1920
Facility closed, 1922; re-opened 1925–1941

New Orleans
O
Gold and Silver
1838
Facility closed, 1861; re-opened 1879–1909[g]

text: Notes[edit]

text:
Jump up ^ The letter "P" is used for the Philadelphia mint mark on all coins (except cents) released from 1980 onward. Before this it had only been used on silver Jefferson nickels from 1942 to 1945.
Jump up ^ Between 1973 and 1986 there was no mint mark (these coins are indistinguishable from coins produced at the Philadelphia Mint from 1973 to 1980); after 1988 the letter "W" was used for coinage, except for the 2009 Ultra High Relief Double Eagle.
Jump up ^ It is now the home of the Nevada State Museum, which still strikes commemorative medallions with the "CC" mint mark (most recently in 2014 commemorating the Nevada Sesquicentennial), using former mint's the original coin press.
Jump up ^ Although the mint mark "D" has been used by two separate mints, it is easy to distinguish between the two, as any 19th century coinage is Dahlonega, and any 20th or 21st century coins are Denver.
Jump up ^ During the period in which this mint branch was operational, The Philippines was an insular territory and then commonwealth of the U.S.; it was the first (and to date only) U.S. branch mint located outside the Continental United States.
Jump up ^ The letter "M" was used for the Manila mint mark on all coins released from 1925 onward; before this it had produced its coins with no mintmark.
Jump up ^ During the Civil War, this mint operated under the control of the State of Louisiana (February 1861) and the Confederate States of America (March 1861) until it ran out of bullion later in that year; some Half Dollars have been identified as being the issue of the State of Louisiana and the Confederacy.

tag: ol

text: Banknotes[edit]

text:
Denomination
Front
Reverse
Portrait
Reverse motif
First series
Latest series
Circulation

One Dollar

George Washington
Great Seal of the United States
Series 1935
Series 2017[50]
Wide

Two Dollars

Thomas Jefferson
Trumbull's Declaration of Independence
Series 1976
Series 2013
Limited

Five Dollars

Abraham Lincoln
Lincoln Memorial
Series 2006
Series 2013
Wide

Ten Dollars

Alexander Hamilton
U.S. Treasury
Series 2004A
Series 2013
Wide

Twenty Dollars

Andrew Jackson
White House
Series 2004
Series 2013
Wide

Fifty Dollars

Ulysses S. Grant
United States Capitol
Series 2004
Series 2013
Wide

One Hundred Dollars

Benjamin Franklin
Independence Hall
Series 2009
Series 2013
Wide

text: The U.S. Constitution provides that Congress shall have the power to "borrow money on the credit of the United States".[51] Congress has exercised that power by authorizing Federal Reserve Banks to issue Federal Reserve Notes. Those notes are "obligations of the United States" and "shall be redeemed in lawful money on demand at the Treasury Department of the United States, in the city of Washington, District of Columbia, or at any Federal Reserve bank".[52] Federal Reserve Notes are designated by law as "legal tender" for the payment of debts.[53] Congress has also authorized the issuance of more than 10 other types of banknotes, including the United States Note[54] and the Federal Reserve Bank Note. The Federal Reserve Note is the only type that remains in circulation since the 1970s.

text: Currently printed denominations are $1, $2, $5, $10, $20, $50, and $100. Notes above the $100 denomination stopped being printed in 1946 and were officially withdrawn from circulation in 1969. These notes were used primarily in inter-bank transactions or by organized crime; it was the latter usage that prompted President Richard Nixon to issue an executive order in 1969 halting their use. With the advent of electronic banking, they became less necessary. Notes in denominations of $500, $1,000, $5,000, $10,000, and $100,000 were all produced at one time; see large denomination bills in U.S. currency for details. With the exception of the $100,000 bill (which was only issued as a Series 1934 Gold Certificate and was never publicly circulated; thus it is illegal to own), these notes are now collectors' items and are worth more than their face value to collectors.

text: Though still predominantly green, post-2004 series incorporate other colors to better distinguish different denominations. As a result of a 2008 decision in an accessibility lawsuit filed by the American Council of the Blind, the Bureau of Engraving and Printing is planning to implement a raised tactile feature in the next redesign of each note, except the $1 and the current version of the $100 bill. It also plans larger, higher-contrast numerals, more color differences, and distribution of currency readers to assist the visually impaired during the transition period.[55]

text: Means of issue[edit]

text: The monetary base consists of coins and Federal Reserve Notes in circulation outside the Federal Reserve Banks and the U.S. Treasury, plus deposits held by depository institutions at Federal Reserve Banks. The adjusted monetary base has increased from approximately 400 billion dollars in 1994, to 800 billion in 2005, and over 3000 billion in 2013.[56] The amount of cash in circulation is increased (or decreased) by the actions of the Federal Reserve System. Eight times a year, the 12-person Federal Open Market Committee meets to determine U.S. monetary policy.[57] Every business day, the Federal Reserve System engages in Open market operations to carry out that monetary policy.[58] If the Federal Reserve desires to increase the money supply, it will buy securities (such as U.S. Treasury Bonds) anonymously from banks in exchange for dollars. Conversely, it will sell securities to the banks in exchange for dollars, to take dollars out of circulation.[59]

text: When the Federal Reserve makes a purchase, it credits the seller's reserve account (with the Federal Reserve). This money is not transferred from any existing funds—it is at this point that the Federal Reserve has created new high-powered money. Commercial banks can freely withdraw in cash any excess reserves from their reserve account at the Federal Reserve. To fulfill those requests, the Federal Reserve places an order for printed money from the U.S. Treasury Department.[60] The Treasury Department in turn sends these requests to the Bureau of Engraving and Printing (to print new dollar bills) and the Bureau of the Mint (to stamp the coins).

text: Usually, the short-term goal of open market operations is to achieve a specific short-term interest rate target. In other instances, monetary policy might instead entail the targeting of a specific exchange rate relative to some foreign currency or else relative to gold. For example, in the case of the United States the Federal Reserve targets the federal funds rate, the rate at which member banks lend to one another overnight. The other primary means of conducting monetary policy include: (i) Discount window lending (as lender of last resort); (ii) Fractional deposit lending (changes in the reserve requirement); (iii) Moral suasion (cajoling certain market players to achieve specified outcomes); (iv) "Open mouth operations" (talking monetary policy with the market).

text: Value[edit]

text:
Buying power of one U.S. dollar compared to 1774 USD

 Year
 Equivalent  buying power

1774
 $1.00

1780
 $0.59

1790
 $0.89

1800
 $0.64

1810
 $0.66

1820
 $0.69

1830
 $0.88

1840
 $0.94

1850
 $1.03

1860
 $0.97

 Year
 Equivalent  buying power

1870
 $0.62

1880
 $0.79

1890
 $0.89

1900
 $0.96

1910
 $0.85

1920
 $0.39

1930
 $0.47

1940
 $0.56

1950
 $0.33

1960
 $0.26

 Year
 Equivalent  buying power

1970
 $0.20

1980
 $0.10

1990
 $0.06

2000
 $0.05

2007
 $0.04

2008
 $0.04

2009
 $0.04

2010
 $0.035

2011
 $0.034

2012
 $0.03

text: The 6th paragraph of Section 8 of Article 1 of the U.S. Constitution provides that the U.S. Congress shall have the power to "coin money" and to "regulate the value" of domestic and foreign coins. Congress exercised those powers when it enacted the Coinage Act of 1792. That Act provided for the minting of the first U.S. dollar and it declared that the U.S. dollar shall have "the value of a Spanish milled dollar as the same is now current".[61]

text: The table to the right shows the equivalent amount of goods that, in a particular year, could be purchased with $1. The table shows that from 1774 through 2012 the U.S. dollar has lost about 97.0% of its buying power.[62]

text: The decline in the value of the U.S. dollar corresponds to price inflation, which is a rise in the general level of prices of goods and services in an economy over a period of time.[63] A consumer price index (CPI) is a measure estimating the average price of consumer goods and services purchased by households. The United States Consumer Price Index, published by the Bureau of Labor Statistics, is a measure estimating the average price of consumer goods and services in the United States.[64] It reflects inflation as experienced by consumers in their day-to-day living expenses.[65] A graph showing the U.S. CPI relative to 1982–1984 and the annual year-over-year change in CPI is shown at right.

text: The value of the U.S. dollar declined significantly during wartime, especially during the American Civil War, World War I, and World War II.[66] The Federal Reserve, which was established in 1913, was designed to furnish an "elastic" currency subject to "substantial changes of quantity over short periods", which differed significantly from previous forms of high-powered money such as gold, national bank notes, and silver coins.[67] Over the very long run, the prior gold standard kept prices stable—for instance, the price level and the value of the U.S. dollar in 1914 was not very different from the price level in the 1880s. The Federal Reserve initially succeeded in maintaining the value of the U.S. dollar and price stability, reversing the inflation caused by the First World War and stabilizing the value of the dollar during the 1920s, before presiding over a 30% deflation in U.S. prices in the 1930s.[68]

text: Under the Bretton Woods system established after World War II, the value of gold was fixed to $35 per ounce, and the value of the U.S. dollar was thus anchored to the value of gold. Rising government spending in the 1960s, however, led to doubts about the ability of the United States to maintain this convertibility, gold stocks dwindled as banks and international investors began to convert dollars to gold, and as a result the value of the dollar began to decline. Facing an emerging currency crisis and the imminent danger that the United States would no longer be able to redeem dollars for gold, gold convertibility was finally terminated in 1971 by President Nixon, resulting in the "Nixon shock".[69]

text: The value of the U.S. dollar was therefore no longer anchored to gold, and it fell upon the Federal Reserve to maintain the value of the U.S. currency. The Federal Reserve, however, continued to increase the money supply, resulting in stagflation and a rapidly declining value of the U.S. dollar in the 1970s. This was largely due to the prevailing economic view at the time that inflation and real economic growth were linked (the Phillips curve), and so inflation was regarded as relatively benign.[69] Between 1965 and 1981, the U.S. dollar lost two thirds of its value.[62]

text: In 1979, President Carter appointed Paul Volcker Chairman of the Federal Reserve. The Federal Reserve tightened the money supply and inflation was substantially lower in the 1980s, and hence the value of the U.S. dollar stabilized.[69]

text: Over the thirty-year period from 1981 to 2009, the U.S. dollar lost over half its value.[62] This is because the Federal Reserve has targeted not zero inflation, but a low, stable rate of inflation—between 1987 and 1997, the rate of inflation was approximately 3.5%, and between 1997 and 2007 it was approximately 2%. The so-called "Great Moderation" of economic conditions since the 1970s is credited to monetary policy targeting price stability.[70]

text: There is ongoing debate about whether central banks should target zero inflation (which would mean a constant value for the U.S. dollar over time) or low, stable inflation (which would mean a continuously but slowly declining value of the dollar over time, as is the case now). Although some economists are in favor of a zero inflation policy and therefore a constant value for the U.S. dollar,[68] others contend that such a policy limits the ability of the central bank to control interest rates and stimulate the economy when needed.[71]

text: Exchange rates[edit]

text: Historical exchange rates[edit]

text:
Currency units per U.S. dollar, averaged over the year

19702
19802
19852
19902
1993
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015[72]

Euro
 —
 —
 —
 —
 —
0.9387
1.0832
1.1171
1.0578
0.8833
0.8040
0.8033
0.7960
0.7293
0.6791
0.7176
0.6739
0.7178
0.7777
0.7530
0.7520
0.9015

Japanese yen
357.6
240.45
250.35
146.25
111.08
113.73
107.80
121.57
125.22
115.94
108.15
110.11
116.31
117.76
103.39
93.68
87.78
79.70
79.82
97.60
105.74
121.05

Pound sterling
8s 4d
=0.4167
0.4484[73]
0.8613[73]
0.6207
0.6660
0.6184
0.6598
0.6946
0.6656
0.6117
0.5456
0.5493
0.5425
0.4995
0.5392
0.6385
0.4548
0.6233
0.6308
0.6393
0.6066
0.6544

Canadian dollar
1.081
1.168
1.321
1.1605
1.2902
1.4858
1.4855
1.5487
1.5704
1.4008
1.3017
1.2115
1.1340
1.0734
1.0660
1.1412
1.0298
0.9887
0.9995
1.0300
1.1043
1.2789

Mexican peso
0.01250–0.026501
2.801
2.671
2.501
3.1237
9.553
9.459
9.337
9.663
10.793
11.290
10.894
10.906
10.928
11.143
13.498
12.623
12.427
13.154
12.758
13.302
15.837

Renminbi yuan
2.46
1.7050
2.9366
4.7832
5.7620
8.2783
8.2784
8.2770
8.2771
8.2772
8.2768
8.1936
7.9723
7.6058
6.9477
6.8307
6.7696
6.4630
6.3093
6.1478
6.1620
6.2840

Indian rupee
7.56
8.000
12.38
16.96
31.291
43.13
45.00
47.22
48.63
46.59
45.26
44.00
45.19
41.18
43.39
48.33
45.65
46.58
53.37
58.51
62.00
64.1332

Singapore dollar
 —
 —
2.179
1.903
1.6158
1.6951
1.7361
1.7930
1.7908
1.7429
1.6902
1.6639
1.5882
1.5065
1.4140
1.4543
1.24586
1.2565
1.2492
1.2511
1.2665
1.3748

South African rand
0.7182
0.7780
2.2343[74]
2.5600
3.2729
6.1191
6.9468
8.6093
10.5176
7.5550
6.4402
6.3606
6.7668
7.0477
8.2480
8.4117
7.3159
7.2510
8.2014
9.6436
10.8420
12.7759

text:
Notes:
1. Mexican peso values prior to 1993 revaluation
2. Value at the start of the year

text: Sources:

text:
US: Last 4 years, 2009–2012, 2005–2008, 2001–2004, 1997–2000, 1993–1996, all available years[75]
Multiple countries: 2004–present
Australia: 1970–present
China: 1974–1991, 1993–1995
Mexico: 1976–1991
Canada: 1977–1991

text: Current exchange rates[edit]

text:
Current USD exchange rates

From Google Finance:
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document_title: Energy

question_text: sound is a form of what kind of energy

question_tokens: sound is a form of what kind of energy

root

text: Energy

text: Forms

text: This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (September 2016) (Learn how and when to remove this template message)

tag: table

text: The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways. Kinetic energy is determined by the movement of an object -- or the composite motion of the components of an object - and potential energy reflects the potential of an object to have motion, and generally is a function of the position of an object within a field or may stored in the field itself.

tag: p

text: While these two categories are sufficient to describe all forms of energy, it is often convenient refer to particular combinations of potential and kinetic energy as its own form. For example, macroscopic mechanical energy is the sum of translational and rotational kinetic and potential energy in a system neglects the kinetic energy due to temperature, and nuclear energy which combines utilize potentials from the nuclear force and the weak force), among others.

text:
Some forms of energy (that an object or system can have as a measurable property)

Type of energy
Description

Mechanical
the sum of macroscopic translational and rotational kinetic and potential energies

Electric
potential energy due to or stored in electric fields

Magnetic
potential energy due to or stored in magnetic fields

Gravitational
potential energy due to or stored in gravitational fields

Chemical
potential energy due to chemical bonds

Ionization
potential energy that binds an electron to its atom or molecule

Nuclear
potential energy that binds nucleons to form the atomic nucleus (and nuclear reactions)

Chromodynamic
potential energy that binds quarks to form hadrons

Elastic
potential energy due to the deformation of a material (or its container) exhibiting a restorative force

Mechanical wave
kinetic and potential energy in an elastic material due to a propagated deformational wave

Sound wave
kinetic and potential energy in a fluid due to a sound propagated wave (a particular form of mechanical wave)

Radiant
potential energy stored in the fields of propagated by electromagnetic radiation, including light

Rest
potential energy due to an object's rest mass

Thermal
kinetic energy of the microscopic motion of particles, a form of disordered equivalent of mechanical energy

text: History

text: The word energy derives from the Ancient Greek: ἐνέργεια, translit. energeia, lit. 'activity, operation',[1] which possibly appears for the first time in the work of Aristotle in the 4th century BC. In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure.

text: In the late 17th century, Gottfried Leibniz proposed the idea of the Latin: vis viva, or living force, which defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, although it would be more than a century until this was generally accepted. The modern analog of this property, kinetic energy, differs from vis viva only by a factor of two.

text: In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its modern sense.[2] Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy". The law of conservation of energy was also first postulated in the early 19th century, and applies to any isolated system. It was argued for some years whether heat was a physical substance, dubbed the caloric, or merely a physical quantity, such as momentum. In 1845 James Prescott Joule discovered the link between mechanical work and the generation of heat.

text: These developments led to the theory of conservation of energy, formalized largely by William Thomson (Lord Kelvin) as the field of thermodynamics. Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. It also led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.[3] Thus, since 1918, theorists have understood that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.

text: Units of measure

text: In 1843, James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. The most famous of them used the "Joule apparatus": a descending weight, attached to a string, caused rotation of a paddle immersed in water, practically insulated from heat transfer. It showed that the gravitational potential energy lost by the weight in descending was equal to the internal energy gained by the water through friction with the paddle.

text: In the International System of Units (SI), the unit of energy is the joule, named after James Prescott Joule. It is a derived unit. It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one metre. However energy is also expressed in many other units not part of the SI, such as ergs, calories, British Thermal Units, kilowatt-hours and kilocalories, which require a conversion factor when expressed in SI units.

text: The SI unit of energy rate (energy per unit time) is the watt, which is a joule per second. Thus, one joule is one watt-second, and 3600 joules equal one watt-hour. The CGS energy unit is the erg and the imperial and US customary unit is the foot pound. Other energy units such as the electronvolt, food calorie or thermodynamic kcal (based on the temperature change of water in a heating process), and BTU are used in specific areas of science and commerce.

text: Scientific use

text: Classical mechanics

text:
Part of a series of articles about

Classical mechanics

F
→

=
m

a
→

{\displaystyle {\vec {F}}=m{\vec {a}}}

Second law of motion

History
Timeline

Branches[show]

Applied
Celestial
Continuum
Dynamics
Kinematics
Kinetics
Statics
Statistical

Fundamentals[show]

Acceleration
Angular momentum
Couple
D'Alembert's principle
Energy

kinetic
potential

Force
Frame of reference
Impulse
Inertia / Moment of inertia
Mass

Mechanical power
Mechanical work

Moment
Momentum
Space
Speed
Time
Torque
Velocity
Virtual work

Formulations[show]

Newton's laws of motion

Analytical mechanics

Lagrangian mechanics
Hamiltonian mechanics
Routhian mechanics
Hamilton–Jacobi equation
Appell's equation of motion
Udwadia–Kalaba equation
Koopman–von Neumann mechanics

Core topics[show]

Damping (ratio)
Displacement
Equations of motion
Euler's laws of motion
Fictitious force
Friction
Harmonic oscillator

Inertial / Non-inertial reference frame
Mechanics of planar particle motion

Motion (linear)
Newton's law of universal gravitation
Newton's laws of motion
Relative velocity
Rigid body

dynamics
Euler's equations

Simple harmonic motion
Vibration

Rotation[show]

Circular motion
Rotating reference frame
Centripetal force
Centrifugal force

reactive

Coriolis force
Pendulum
Tangential speed
Rotational speed

Angular acceleration / displacement / frequency / velocity

Scientists[show]

Galileo
Huygens
Newton
Kepler
Horrocks
Halley
Euler
d'Alembert
Clairaut
Lagrange
Laplace
Hamilton
Poisson
Daniel Bernoulli
Johann Bernoulli
Cauchy

v
t
e

text: In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity. Several formulations of mechanics have been developed using energy as a core concept.

text: Work, a function of energy, is force times distance.

text:
This says that the work (

W

{\displaystyle W}

) is equal to the line integral of the force F along a path C; for details see the mechanical work article. Work and thus energy is frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball.

text: The total energy of a system is sometimes called the Hamiltonian, after William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.[4]

text: Another energy-related concept is called the Lagrangian, after Joseph-Louis Lagrange. This formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of motion or be derived from them. It was invented in the context of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy. Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction).

text: Noether's theorem (1918) states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalisation of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.

text: Chemistry

text: In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved. Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thus the products of a reaction may have more or less energy than the reactants. A reaction is said to be exergonic if the final state is lower on the energy scale than the initial state; in the case of endergonic reactions the situation is the reverse. Chemical reactions are invariably not possible unless the reactants surmount an energy barrier known as the activation energy. The speed of a chemical reaction (at given temperature T) is related to the activation energy E, by the Boltzmann's population factor e−E/kT – that is the probability of molecule to have energy greater than or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation.The activation energy necessary for a chemical reaction can be in the form of thermal energy.

text: Biology

text: In biology, energy is an attribute of all biological systems from the biosphere to the smallest living organism. Within an organism it is responsible for growth and development of a biological cell or an organelle of a biological organism. Energy is thus often said to be stored by cells in the structures of molecules of substances such as carbohydrates (including sugars), lipids, and proteins, which release energy when reacted with oxygen in respiration. In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human metabolism, assuming an average human energy expenditure of 12,500 kJ per day and a basal metabolic rate of 80 watts. For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts is about the maximum.[5] The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a "feel" for the use of a given amount of energy.[6]

text: Sunlight's radiant energy is also captured by plants as chemical potential energy in photosynthesis, when carbon dioxide and water (two low-energy compounds) are converted into the high-energy compounds carbohydrates, lipids, and proteins. Plants also release oxygen during photosynthesis, which is utilized by living organisms as an electron acceptor, to release the energy of carbohydrates, lipids, and proteins. Release of the energy stored during photosynthesis as heat or light may be triggered suddenly by a spark, in a forest fire, or it may be made available more slowly for animal or human metabolism, when these molecules are ingested, and catabolism is triggered by enzyme action.

text: Any living organism relies on an external source of energy—radiant energy from the Sun in the case of green plants, chemical energy in some form in the case of animals—to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and food molecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) are convenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria

text: and some of the energy is used to convert ADP into ATP.

text: The rest of the chemical energy in O2[7] and the carbohydrate or fat is converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains is used for other metabolism when ATP reacts with OH groups and eventually splits into ADP and phosphate (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for work:[note 2]

text: It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the energy they receive (chemical or radiant energy), and it is true that most real machines manage higher efficiencies. In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to the molecules it is built from. The second law of thermodynamics states that energy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across the remainder of the universe ("the surroundings").[note 3] Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy ecological niches that are not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology: to take just the first step in the food chain, of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis, 64.3 Pg/a (52%) are used for the metabolism of green plants,[8] i.e. reconverted into carbon dioxide and heat.

text: Earth sciences

text: In geology, continental drift, mountain ranges, volcanoes, and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior,[9] while meteorological phenomena like wind, rain, hail, snow, lightning, tornadoes and hurricanes are all a result of energy transformations brought about by solar energy on the atmosphere of the planet Earth.

text: Sunlight may be stored as gravitational potential energy after it strikes the Earth, as (for example) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbines or generators to produce electricity). Sunlight also drives many weather phenomena, save those generated by volcanic events. An example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddenly to power a few days of violent air movement.

text: In a slower process, radioactive decay of atoms in the core of the Earth releases heat. This thermal energy drives plate tectonics and may lift mountains, via orogenesis. This slow lifting represents a kind of gravitational potential energy storage of the thermal energy, which may be later released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars created these atoms.

text: Cosmology

text: In cosmology and astronomy the phenomena of stars, nova, supernova, quasars and gamma-ray bursts are the universe's highest-output energy transformations of matter. All stellar phenomena (including solar activity) are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter (usually molecular hydrogen) into various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter elements, primarily hydrogen). The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang. At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight.

text: Quantum mechanics

text:
In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation:

E
=
h
ν

{\displaystyle E=h\nu }

 (where

h

{\displaystyle h}

 is Planck's constant and

ν

{\displaystyle \nu }

 the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

text: Relativity

text: When calculating kinetic energy (work to accelerate a massive body from zero speed to some finite speed) relativistically – using Lorentz transformations instead of Newtonian mechanics – Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it rest energy: energy which every massive body must possess even when being at rest. The amount of energy is directly proportional to the mass of the body:

text: where

text: For example, consider electron–positron annihilation, in which the rest energy of these two individual particles (equivalent to their rest mass) is converted to the radiant energy of the photons produced in the process. In this system the matter and antimatter (electrons and positrons) are destroyed and changed to non-matter (the photons). However, the total mass and total energy do not change during this interaction. The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from the radiant energy of two (or more) annihilating photons.

text: In general relativity, the stress–energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.[10]

text: Energy and mass are manifestations of one and the same underlying physical property of a system. This property is responsible for the inertia and strength of gravitational interaction of the system ("mass manifestations"), and is also responsible for the potential ability of the system to perform work or heating ("energy manifestations"), subject to the limitations of other physical laws.

text: In classical physics, energy is a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy–momentum 4-vector).[10] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts).

text: Transformation

text:
Some forms of transfer of energy ("energy in transit") from one object or system to another

Type of transfer process
Description

Heat
that amount of thermal energy in transit spontaneously towards a lower-temperature object

Work
that amount of energy in transit due to a displacement in the direction of an applied force

Transfer of material
that amount of energy carried by matter that is moving from one system to another

text: Energy may be transformed between different forms at various efficiencies. Items that transform between these forms are called transducers. Examples of transducers include a battery, from chemical energy to electric energy; a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) and ultimately to electric energy through an electric generator; or a heat engine, from heat to work.

text: Examples of energy transformation include generating electric energy from heat energy via a steam turbine, or lifting an object against gravity using electrical energy driving a crane motor. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground. Our Sun transforms nuclear potential energy to other forms of energy; its total mass does not decrease due to that in itself (since it still contains the same total energy even if in different forms), but its mass does decrease when the energy escapes out to its surroundings, largely as radiant energy.

text: There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

text: Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

text:
Energy is also transferred from potential energy (

E

p

{\displaystyle E_{p}}

) to kinetic energy (

E

k

{\displaystyle E_{k}}

) and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

text:
E

p
i

+

E

k
i

=

E

p
F

+

E

k
F

{\displaystyle E_{pi}+E_{ki}=E_{pF}+E_{kF}}

(4)

text:
The equation can then be simplified further since

E

p

=
m
g
h

{\displaystyle E_{p}=mgh}

 (mass times acceleration due to gravity times the height) and

E

k

=

1
2

m

v

2

{\displaystyle E_{k}={\frac {1}{2}}mv^{2}}

 (half mass times velocity squared). Then the total amount of energy can be found by adding

E

p

+

E

k

=

E

t
o
t
a
l

{\displaystyle E_{p}+E_{k}=E_{total}}

.

text: Conservation of energy and mass in transformation

text: Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

text:
Part of the rest energy (equivalent to rest mass) of matter may be converted to other forms of energy (still exhibiting mass), but neither energy nor mass can be destroyed; rather, both remain constant during any process. However, since

c

2

{\displaystyle c^{2}}

 is extremely large relative to ordinary human scales, the conversion of an everyday amount of rest mass (for example, 1 kg) from rest energy to other forms of energy (such as kinetic energy, thermal energy, or the radiant energy carried by light and other radiation) can liberate tremendous amounts of energy (~

9
×

10

16

{\displaystyle 9\times 10^{16}}

 joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of an everyday amount energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure on a weighing scale, unless the energy loss is very large. Examples of large transformations between rest energy (of matter) and other forms of energy (e.g., kinetic energy into particles with rest mass) are found in nuclear physics and particle physics.

text: Reversible and non-reversible transformations

text: Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

text: As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

text: Conservation of energy

text: The fact that energy can be neither created nor be destroyed is called the law of conservation of energy. In the form of the first law of thermodynamics, this states that a closed system's energy is constant unless energy is transferred in or out by work or heat, and that no energy is lost in transfer. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.[11]

text: While heat can always be fully converted into work in a reversible isothermal expansion of an ideal gas, for cyclic processes of practical interest in heat engines the second law of thermodynamics states that the system doing work always loses some energy as waste heat. This creates a limit to the amount of heat energy that can do work in a cyclic process, a limit called the available energy. Mechanical and other forms of energy can be transformed in the other direction into thermal energy without such limitations.[12] The total energy of a system can be calculated by adding up all forms of energy in the system.

text: Richard Feynman said during a 1961 lecture:[13]

text: There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

text: Most kinds of energy (with gravitational energy being a notable exception)[14] are subject to strict local conservation laws as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.[12][13]

text: This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation of energy is a mathematical consequence of translational symmetry of time,[15] a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

text: Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appears as system mass, whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it.

text: In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by

text: which is similar in form to the Heisenberg Uncertainty Principle (but not really mathematically equivalent thereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

text: In particle physics, this inequality permits a qualitative understanding of virtual particles which carry momentum, exchange by which and with real particles, is responsible for the creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanical energy state of photons) are also responsible for electrostatic interaction between electric charges (which results in Coulomb law), for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, for van der Waals bond forces and some other observable phenomena.

text: Energy transfer

text: Closed systems

text: Energy transfer can be considered for the special case of systems which are closed to transfers of matter. The portion of the energy which is transferred by conservative forces over a distance is measured as the work the source system does on the receiving system. The portion of the energy which does not do work during the transfer is called heat.[note 4] Energy can be transferred between systems in a variety of ways. Examples include the transmission of electromagnetic energy via photons, physical collisions which transfer kinetic energy,[note 5] and the conductive transfer of thermal energy.

text: Energy is strictly conserved and is also locally conserved wherever it can be defined. In thermodynamics, for closed systems, the process of energy transfer is described by the first law:[note 6]

text:
Δ

E
=
W
+
Q

{\displaystyle \Delta {}E=W+Q}

(1)

text:
where

E

{\displaystyle E}

 is the amount of energy transferred,

W

{\displaystyle W}

  represents the work done on the system, and

Q

{\displaystyle Q}

 represents the heat flow into the system. As a simplification, the heat term,

Q

{\displaystyle Q}

, is sometimes ignored, especially when the thermal efficiency of the transfer is high.

text:
Δ

E
=
W

{\displaystyle \Delta {}E=W}

(2)

text: This simplified equation is the one used to define the joule, for example.

text: Open systems

text:
Beyond the constraints of closed systems, open systems can gain or lose energy in association with matter transfer (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). Denoting this energy by

E

{\displaystyle E}

, one may write

text:
Δ

E
=
W
+
Q
+
E
.

{\displaystyle \Delta {}E=W+Q+E.}

(3)

text: Thermodynamics

text: Internal energy

text: Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.[16]

text: First law of thermodynamics

text: The first law of thermodynamics asserts that energy (but not necessarily thermodynamic free energy) is always conserved[17] and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a commonly used corollary of the first law is that, for a system subject only to pressure forces and heat transfer (e.g., a cylinder-full of gas) without chemical changes, the differential change in the internal energy of the system (with a gain in energy signified by a positive quantity) is given as

text: where the first term on the right is the heat transferred into the system, expressed in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated), and the last term on the right hand side is identified as work done on the system, where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system).

text: This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat and pV-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a closed system is expressed in a general form by

text:
where

δ
Q

{\displaystyle \delta Q}

 is the heat supplied to the system and

δ
W

{\displaystyle \delta W}

 is the work applied to the system.

text: Equipartition of energy

text: The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential. At two points in the oscillation cycle it is entirely kinetic, and at two points it is entirely potential. Over the whole cycle, or over many cycles, net energy is thus equally split between kinetic and potential. This is called equipartition principle; total energy of a system with many degrees of freedom is equally split among all available degrees of freedom.

text: This principle is vitally important to understanding the behaviour of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available energy states that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is called the second law of thermodynamics. The second law of thermodynamics is valid only for systems which are near or in equilibrium state. For non-equilibrium systems, the laws governing system’s behavior are still debatable. One of the guiding principles for these systems is the principle of maximum entropy production.[18][19] It states that nonequilibrium systems behave in such a way to maximize its entropy production.[20]