# Specific Heat Capacity at Constant Pressure

on . Posted in Thermodynamics

Specific heat capacity at constant pressur, abbreviated as $$C_p$$, is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius while keeping the pressure constant.  It measures the ability of a substance to absorb heat energy at a constant pressure without undergoing a phase change (melting or boiling).

It's important to note that specific heat capacity at constant pressure differs from specific heat capacity at constant volume.  The key difference is that $$C_p$$ assumes that the pressure remains constant during the heating process, while $$C_v$$ assumes that the volume remains constant.  For many gases, $$C_p$$ is greater than $$C_v$$ because at constant pressure, heat is not only used to increase the temperature but also to do work on the gas as it expands.

The specific heat capacity values are used in thermodynamics and heat transfer calculations, helping to determine how substances respond to changes in temperature and pressure.  They vary from one substance to another and can be experimentally determined for different materials.

## Specific Heat Capacity at Constant Pressure Formula

$$\large{ C_p = \left(\frac{ \partial H }{ \partial T }\right)_p }$$
Symbol English Metric
$$\large{ C_p }$$ = heat constant pressure  $$\large{ \frac{Btu}{F} }$$   $$\large{ \frac{kJ}{K} }$$
$$\large{ \partial H }$$ = enthalpy rate of change  $$\large{ \frac{Btu}{lbm} }$$   $$\large{ \frac{kJ}{kg} }$$
$$\large{ p }$$ = pressure  $$\large{ \frac{lbf}{in^2} }$$  $$\large{ Pa }$$
$$\large{ \partial T }$$ = temperature rate of change $$\large{ F }$$ $$\large{ K }$$
$$\large{ \partial }$$ = designates heat as a path function $$\large{ \frac{Btu}{lbm} }$$ $$\large{ \frac{kJ}{kg} }$$ 