Abstract
Specific heat is usually analyzed only for common thermodynamic processes, leaving us with the impression that it can always be expressed as a single-valued function of temperature. In this paper, we show that specific heat functions may be multivalued even for processes that are mathematically simple, such as an ideal gas following a linear path with a negative slope in the pressure–volume diagram. Although this example has been studied previously, we show that the multivalued approach provides additional physical insights, and we establish the conditions that any path must satisfy in order to have a single-valued specific heat. As a final application of our approach, we demonstrate a geometric theorem.
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