Entropy
Isothermal expansion or compression of an ideal gas

For the expansion (or compression) of an ideal gas from an initial volume V 0 {\textstyle V_{0}} and pressure P 0 {\textstyle P_{0}} to a final volume V {\textstyle V} and pressure P {\textstyle P} at any constant temperature, the change in entropy is given by: Δ S = n R ln V V 0 = − n R ln P P 0 {\displaystyle \Delta S=nR\ln {\frac {V}{V_{0}}}=-nR\ln {\frac {P}{P_{0}}}} Here n {\textstyle n} is the amount of gas (in moles) and R {\textstyle R} is the ideal gas constant. These equations also apply for expansion into a finite vacuum or a throttling process, where the temperature, internal energy and enthalpy for an ideal gas remain constant.
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