Enthalpy and Heat Capacity

Enthalpy (H) is a thermodynamic quantity that combines the internal energy of a system with the product of its pressure and volume. It can be mathematically represented as H = U + pV, where U is the internal energy, p is the pressure, and V is the volume. Since energy, pressure, and volume are state functions, enthalpy is also a state function. However, it's important to note that absolute enthalpy values for specific substances cannot be measured. Only the change in enthalpy, denoted as ΔH, can be determined.

When a system undergoes a process at constant pressure, the change in enthalpy (ΔH) equals the heat (q) gained or lost by the system. For example, if a system loses energy to the surroundings in the form of heat — such as during the combustion of wood — the surrounding temperature rises. This heat loss is indicated by a negative sign convention for q, making ΔH negative. The process is therefore described as exothermic. Conversely, when a system gains energy from the surroundings in the form of heat — like in a chemical cold pack — the surrounding temperature falls. Here, heat is indicated by a positive sign, making ΔH positive, and the process is termed endothermic.

To understand heat capacity, let's consider two identical cylinders, A and B, both filled with an ideal gas but held under different conditions. Cylinder A is sealed, meaning its volume doesn't change when heated - all the heat goes into increasing the system's internal energy. Cylinder B, however, allows for expansion when heated, using heat for both the work done in the gas's expansion and increasing the system's internal energy.

For cylinder A, the internal energy increases with increasing temperature at constant volume. For cylinder B, the energy supplied as heat at constant pressure is equal to the change in enthalpy. The enthalpy of a substance increases as its temperature is raised.

The slope of the tangents to the plots of enthalpy against temperature at constant pressure (C_p) and internal energy against temperature at constant volume (C_v) defines two distinct heat capacities.

Heat capacity, denoted as C, is the amount of heat required to raise the temperature of a substance by one degree Celsius. Dividing the heat capacity by the moles of the substance gives the molar heat capacity. While heat capacity is an extensive property (depending on the amount of substance), molar heat capacity is an intensive property (independent of the amount of substance).