The classical Carnot heat engine
Real gases experience a temperature change during free expansion. For an ideal gas, the temperature doesn't change, and the conditions before and after adiabatic free expansion satisfy
During free expansion, no work is done by the gas. The gas goes through states that are not in thermodynamic equilibrium before reaching its final state, which implies that one cannot define thermodynamic parameters as values of the gas as a whole. For example, the pressure changes locally from point to point, and the volume occupied by the gas (which is formed of particles) is not a well defined quantity.
A free expansion is typically achieved by opening a stopcock that allows the gas to expand into a vacuum. Although it would be difficult to achieve in reality, it is instructive to imagine a free expansion caused by moving a piston faster than virtually any atom. No work is done because there is no pressure on the piston. No heat energy leaves or enters the piston. Nevertheless, there is an entropy change. But the well-known formula for entropy change,
- Tipler, P., and Mosca, G. Physics for Scientists and Engineers (with modern physics), 6th edition, 2008. pages 602 and 647
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