An identity for the volume derivative of entropy along an arbitrary reversible path is derived and used to show that the heat to a fluid can attain both positive and negative values along certain negatively sloped paths in the pressure-volume plane. A temperature-entropy plot graphically illustrates this point. An analogous entropy identity for magnetic systems is derived and used together with a temperature-entropy plot to gain insights into paramagnetic behavior. In contrast with the ideal gas, a path for an ideal paramagnet can have both positive and negative heats only if it attains both positive and negative slopes in a magnetization vs magnetic field plot. (C) 1995 American Association of Physics Teachers. [References: 10]
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