# Heat capacity

A2 Physics

Specific heat capacity, c, is the energy required to raise the temperature of a unit mass of a substance by 1 K without a change of state. This is measured in Jkg-1K-1.

This is measured using conservation of energy, using gravitation potential in the inversion tube experiment or electrical potential.

University Chemistry and Physics

Using lower case c denotes specific heat capacity, while upper case C is molar heat capacity. Where C is used, n (moles) is used instead of m (mass).

There are two types of heat capacity: heat capacity at constant volume, CV, and heat capacity at constant pressure, CP.

We can write the above equation in terms of differentials:

This means that:

We can use :

from the equipartition principle.

So at constant volume:

At constant pressure we use the first law of thermodynamics:

To get:

For a solid, each bond can be represented as a spring undergoing simple harmonic motion. There are 3 dimensions and 3 degrees of potential energy, so six degrees of freedom. This means the energy per molecule, E, is:

And the total energy is:

We can see that CP > CV, and that:

We call the ratio CP /CV  the heat capacity ratio or the isentropic expansion factor, γ (Greek letter gamma):

This is used in calculations involving adiabatic processes.