The difference in heat coefficients for constant pressure and constant volume arises from the work done by the system. At constant volume, all added heat contributes to the internal energy, while at constant pressure, some heat is used to perform work by expanding the volume. This makes the heat capacity at constant pressure higher, as the system can accommodate additional heat in more ways. The relationship between these coefficients can be mathematically derived, but the fundamental concept is rooted in the system's flexibility. Understanding this distinction clarifies the behavior of heat transfer under varying conditions.
