Heat capacities vary with temperature and pressure from "summary" of Thermodynamics and an Introduction to Thermostatistics by Herbert B. Callen
The heat capacity of a system is a fundamental property that characterizes its response to changes in temperature and pressure. It quantifies the amount of heat required to raise the temperature of the system by a certain amount. However, it is important to recognize that the heat capacity is not a fixed value, but rather a function of temperature and pressure. As the temperature of a system increases, its heat capacity generally changes as well. This is because the internal energy of the system is a function of temperature, and therefore the amount of heat required to raise the temperature by a certain amount will also vary. In general, the heat capacity tends to increase with temperature, as the system has more degrees of freedom available for storing energy at higher temperatures. Similarly, the heat capacity of a system may also vary with pressure. This is particularly true for systems that undergo phase transitions, such as the melting or boiling of a substance. During such transitions, the heat capacity can exhibit discontinuities or other non-linear behavior as the system reorganizes its internal structure in response to changes in pressure. In general, the variation of heat capacities with temperature and pressure reflects the complex interplay of energy storage mechanisms within a system. These mechanisms can involve changes in the vibrational, rotational, and translational degrees of freedom of the system's constituent particles, as well as interactions between the particles themselves. Understanding how heat capacities vary with temperature and pressure is therefore crucial for accurately predicting the behavior of thermodynamic systems under different conditions. By accounting for these variations, we can develop more accurate models and make more reliable predictions about the behavior of materials and processes in the real world.
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