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:
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.