# first law of thermodynamics

Laws of thermodynamics |
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Zeroth Law |

First Law |

Second Law |

Third Law |

Combined Law |

[ edit ] |

The

**first law of thermodynamics**is an expression of the universal law of conservation of energy, and identifies heat transfer as a form of energy transfer. The most common enunciation of the first law of thermodynamics is:

The increase in the internal energy of a thermodynamic system is equal to the amount of heat energy added to the system minus the work done by the system on the surroundings. |

## History

The first explicit statement of the first law of thermodynamics was given by Rudolf Clausius in 1850: "There is a state function E, called 'energy', whose differential equals the work exchanged with the surroundings during an adiabatic process."

## Mathematical formulation

The mathematical statement of the first law of a closed system is given by:where is the infinitesimal increase in the internal energy of the system, is the infinitesimal amount of heat added to the system, and is the infinitesimal amount of work done by the system on the surroundings. The infinitesimal heat and work are denoted by

**δ**rather than

**d**because, in mathematical terms, they are inexact differentials rather than exact differentials. In other words, there is no function

*Q*or

*W*that can be differentiated to yield δ

*Q*or δ

*W*.

The integral of an inexact differential is path dependent, i.e. it depends upon the particular "path" taken through the space of thermodynamic parameters while the integral of an exact differential depends only upon the initial and final states. If the initial and final states are the same, (i.e. the integral is taken around a closed loop in thermodynamic parameter space) the value of the integral represents the change in the internal energy of the system.

## Reversible processes

An expression of the first law can be written in terms of exact differentials by realizing that the work that a system does is equal to its pressure times the infinitesimal change in its volume. In other words, where is pressure and is volume. For a reversible process, the total amount of heat added to a closed system can be expressed as where is temperature and is entropy. For a reversible process, the first law may now be restated:In the case where the system is not closed, energy may also be brought into the system by the addition of new material. In this case the first law is written:

where is the (small) number of type-i particles added to the system, and is the chemical potential of type-i particles.

## Force-functions

A useful idea, introduced by Willard Gibbs in 1876, is that quantities such as internal energy*U*and Helmholtz free energy

*A*may be regarded as a kind of

**force-function**. For example, the energy gained by a particle is equal to the force applied to the particle multiplied by the displacement of the particle while that force is applied. Now consider the first law without the heating and particle terms: . The pressure

*p*can be viewed as a force (and in fact has units of force per unit area) while is the displacement (with units of distance times area). We may say, with respect to this work term, that a pressure difference forces a transfer of volume, and that the product of the two is the amount of work-energy transferred as a result of the process.

It is useful to view the term in the same light: With respect to this heat term, a temperature difference forces a transfer of entropy, and the product of the two is the amount of heat-energy transferred as a result of the process. Here, the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement.

Similarly, a difference in chemical potential between groups of particles in the system forces a transfer of particles, and the corresponding product is the amount of energy transferred as a result of the process. For example, consider a system consisting of two phases: liquid water and water vapor. There is a generalized "force" of evaporation which drives water molecules out of the liquid. There is a generalized "force" of condensation which drives vapor molecules out of the vapor. Only when these two "forces" (or chemical potentials) are equal will there be equilibrium, and the net transfer will be zero.

The two thermodynamic parameters which form a generalized force-displacement pair are termed "conjugate variables". The two most familiar pairs are, of course, pressure-volume, and temperature-entropy.

## Sign convention

### Physics and Chemistry

In physics and chemistry, the system is the object of greatest interest, and it is natural to talk about the work done on the system by the surroundings. This changes the sign of the equation. Defined in this manner, the first law is a generalization of this concept which states for a thermodynamic cycle that the net heat input is equal to the net work output. For a system with a fixed number of particles (closed system), the first law is stated as:- ,

where

- is an infinitesimal increase in the internal energy of the system,

- is an infinitesimal amount of heat
*added*to the system,

- is an infinitesimal amount of work done on the system, and

- denotes an inexact differential.

### Thermodynamics and Engineering

In thermodynamics and engineering, it is natural to think of the system as a heat engine which does work on the surroundings, and to state that the total energy added by heating is equal to the sum of the increase in internal energy plus the work done by the system. Hence is the amount of energy lost by the system due to work done by the system on its surroundings. During the portion of the thermodynamic cycle where the engine is doing work, is positive, but there will always be a portion of the cycle where is negative, e.g., when the working gas is being compressed. When represents the work done by the system, the first law is written:Very occasionally, the sign on the heat may be inverted, so that is the flow of heat out of the system, and is the work into the system:

Because of this ambiguity, it is vitally important in any discussion involving the first law to explicitly establish the sign convention in use.

## See also

## References

- Goldstein, Martin, and Inge F., 1993.
*The Refrigerator and the Universe*. Harvard Univ. Press. A gentle introduction.

## External links

- 30+ Variations of the 1st Law
- Mechanical Theory of Heat – Nine Memoirs by Rudolf Clausius [1850-1865] on the 1st and 2nd Laws of Thermodynamics.

**laws of thermodynamics**, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. Since their conception, however, these laws have become some of the most important in all of physics and other branches of science connected to thermodynamics.

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The

**second law of thermodynamics**is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.**.....**Click the link for more information.**Thermodynamics**(from the Greek θερμη,

*therme,*meaning "heat" and δυναμις,

*dynamis,*meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on

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**conservation of energy**states that the total amount of energy in any closed system remains constant but can be recreated, although it may change forms, e.g. friction turns kinetic energy into thermal energy.

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In thermodynamics, the

**internal energy**of a thermodynamic system, or a body with well-defined boundaries, denoted by*U*, or sometimes*E*, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and**.....**Click the link for more information. In thermodynamics, a

**thermodynamic system**, originally called a*working substance*, is defined as that part of the universe that is under consideration. A real or imaginary boundary separates the system from the rest of the universe, which is referred to as the environment**.....**Click the link for more information.**Editing of this page by unregistered or newly registered users is currently disabled due to vandalism.**

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In thermodynamics,

**work**is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. It is a generalization of the concept of mechanical work in mechanics.**.....**Click the link for more information. In thermodynamics, a

**thermodynamic system**, originally called a*working substance*, is defined as that part of the universe that is under consideration. A real or imaginary boundary separates the system from the rest of the universe, which is referred to as the environment**.....**Click the link for more information.**mechanical equivalent of heat**was a theory, connected to the theory of heat, developed in about 1843, that heat

*Q*and mechanical work

*W*were equivalent via a proportionality constant

*A*:

^{[2]}

^{[3]}

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**James Prescott Joule**

James Joule - English physicist

Born November 24 1818

Salford, Lancashire, England

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**Rudolf Julius Emanuel Clausius**(January 2, 1822 – August 24, 1888), was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics.

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18th century -

1820s 1830s 1840s - 1850s - 1860s 1870s 1880s

1847 1848 1849 -

**19th century**- 20th century1820s 1830s 1840s - 1850s - 1860s 1870s 1880s

1847 1848 1849 -

**1850**- 1851 1852 1853**:***Subjects:*Archaeology - Architecture -**.....**Click the link for more information.**adiabatic process**or an

**isocaloric process**is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable (from a dia bainein), corresponding here to an absence of heat transfer.

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In thermodynamics, an

**inexact differential**or*imperfect differential*is any quantity, particularly heat Q and work W, that are not state functions, in that their values depend on how the process is carried out.**.....**Click the link for more information.**;**

**;**

These conditions, which are easy to generalize, arise from the independence of the order of differentiations in the calculation of the second derivatives.

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**is a phrase used to mean one of two things (Pierson 2004). Some authors use path-dependence to mean simply "history matters" - a broad conception - while others use it to mean that institutions are self reinforcing - a narrow conception.**

*Path-dependence***.....**Click the link for more information.

**Pressure**(symbol:

*p*) is the force per unit area applied on a surface in a direction perpendicular to that surface.

**Gauge pressure**is the pressure relative to the local atmospheric or ambient pressure.

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The

**volume**of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.**.....**Click the link for more information.**reversible process**, or

*reversible cycle*if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy.

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A

**closed system**is a system in the state of being isolated from the environment. It is often used to refer to a theoretical scenario where perfect closure is an assumption, however in practice no system can be completely closed; there are only varying degrees of closure.**.....**Click the link for more information.**trillion**fold).]]

**Temperature**is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.

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**Ice melting**- a classic example of

*entropy increasing*

^{[1]}described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice.

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**J. Willard Gibbs**

(1839-1903)

Born January 11 1839

New Haven, Connecticut, U.S.

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In thermodynamics, the

**internal energy**of a thermodynamic system, or a body with well-defined boundaries, denoted by*U*, or sometimes*E*, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and**.....**Click the link for more information. In thermodynamics, the

**Helmholtz free energy**is a thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature.**.....**Click the link for more information.**conjugate variables**such as pressure/volume or temperature/entropy. In fact all thermodynamic potentials are expressed in terms of conjugate pairs.

For a mechanical system, a small increment of energy is the product of a force times a small displacement.

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**Physics**is the science of

*matter*

^{[1]}

*and its motion*

^{[2]}

^{[3]}, as well as

*space and time*

^{[4]}

^{[5]}—the science that deals with concepts such as force, energy, mass, and charge.

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