What does a thermodynamic equation of state express in terms of thermodynamic quantities?

A thermodynamic equation of state provides a relationship between different thermodynamic variables for a given substance, and it primarily allows for the calculation of one variable when the others are known. In this context, the correct answer indicates that pressure is expressed as a function of temperature and volume, which is indeed a common formulation in thermodynamics.

This relationship is foundational because it encapsulates how the state of a system can change with variations in temperature and volume, which in turn affect the pressure of the system. For example, the ideal gas law (PV=nRT) is a classic illustration of an equation of state, showing how pressure (P) relates to temperature (T) and volume (V) for an ideal gas.

While temperature, entropy, and volume are important thermodynamic quantities, they do not specifically form a traditional equation of state like pressure does in relation to temperature and volume. Similarly, energy changes in a system and heat capacity at constant pressure are crucial concepts in thermodynamics, but they do not directly define the relationship between state variables in the same way that an equation of state does. Thus, the choice that specifies pressure as a function of temperature and volume accurately captures the essence of what a thermodynamic equation of state represents.