__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^{-1}K^{-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, *C*_{V}, and heat capacity at constant pressure, *C*_{P}.

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 *C*_{P} >* C*_{V}, and that:

We call the ratio *C*_{P} /*C*_{V }the heat capacity ratio or the isentropic expansion factor, *γ *(Greek letter gamma):

This is used in calculations involving adiabatic processes.

Back to Contents: Chemistry: Thermodynamics

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