Conservation of energy

:This article is about the physics principle. For information on using energy resources sustainably, see Energy Conservation.

Mathematical formulations

One formulation for the first law of thermodynamics is

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: Q = Delta U + W

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where Q is heat transferred into the system from the surroundings, W

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is work done by the system, and U is the internal energy of the system.

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This energy is mostly kinetic energy: the potential energy can be assumed to

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be negligible. Pressure-volume work (e.g. done by a gas on a piston) is

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defined to be

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: W = P Delta V.

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Equation (1) can be interpreted as follows: Q is heat energy being

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input into the system. The system then can use this incoming energy

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to do two things: (1) do work, or (2) increase its own internal energy.

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Here is an analogy: Q is income, which can then be spent to buy

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things (W), or it can be saved in a bank account ( Delta U ).

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If all the heat is used to do work ( Q = W and

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Delta U = 0 ) then the system

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is undergoing an isothermal process, which means that its

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temperature remains constant. This is because the system's internal

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energy is proportional to its temperature.

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If all the heat is used to increase internal energy,

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( Q = Delta U and W = 0 )

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then the system is undergoing an

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isochoric process, also called isometric process. This is

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a process in which the system's volume is constant:

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Delta V = 0 so that, according to equation (2),

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W = 0.

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It is also possible for the heat energy to be used up partially by

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doing work and partially by increasing internal energy. An example of

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such processes is the isobaric process.

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Equation (1) is the one preferred by engineers. Another form preferred by chemists is

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: Delta U = Q + W

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where W is work done on the system by the surroundings. In this

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case pressure-volume work is defined to be

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: W = -P Delta V.

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Equation (3) can be interpreted to mean that heat Q and

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work W are energies being transferred into or out of the system.

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The system then responds by increasing its internal energy

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accordingly. In Equation (3) neither Q nor W are state functions. A state function does not depend on which particular thermodynamic process is chosen to connect the initial and final thermostatic states.

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