Heat Capacity Formulas Reference Page

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Intro to Heat Capacity Formulas

In many thermodynamic calculations, we need to determine how the internal energy or enthalpy of a substance changes with temperature. These changes are often calculated using heat capacities.

Heat-capacity relationships allow engineers to compute energy changes for gases and liquids over temperature ranges where phase changes do not occur. The videos on this page explain how heat capacity relates to internal energy and enthalpy, how integrals appear in the calculations, and how empirical correlations such as the Shomate equation can be used for accurate results.

The Enthalpy Games: The Ballad of Integrals and Means

This video explains how heat capacities relate to internal energy and enthalpy and shows how integrals and mean heat capacities are used to compute energy changes over temperature ranges.

Visuals

The Enthalpy Games: Sunrise on the Calculations

This video demonstrates how to perform practical calculations of enthalpy and internal-energy changes using heat-capacity formulas and tabulated correlations.

Visuals

Examples and Definitions

Definitions

Heat Capacity at Constant Volume
The change in specific or molar internal energy with temperature at constant volume for a substance not undergoing a phase change.

\[ C_v \equiv \left(\frac{\partial \hat{U}}{\partial T}\right)_V \]

Heat Capacity at Constant Pressure
The change in specific or molar enthalpy with temperature at constant pressure for a substance not undergoing a phase change.

\[ C_p \equiv \left(\frac{\partial \hat{H}}{\partial T}\right)_P \]

Shomate Equation
An empirical equation used to fit experimental heat-capacity data. One common form is

\[ C_p = a + bT + cT^2 + dT^3 + \frac{e}{T^2} \]

This equation allows accurate calculation of temperature-dependent heat capacities and the associated energy changes.