Entropy and heat along reversible paths for fluids and magnets

Abstract

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.