The relationship between temperature and heat in a solid or liquid

In solids and liquids, which are not undergoing a phase change, the relation between heat in and Temperature change is

where is the specific heat of the object. This is sometimes given as

where is the molar specific heat of the object.

The values of (and ) are different depending on whether the heating process occurs at constant volume or constant pressure.

Explanation

so if is constant, . However if we keep constant, so some heat gets spent as work.

Note that at Phase change boundaries, it is impossible to increase temperature. See Heat of transformation.

Ideal gas

Proof

For constant , we have . It follows . Hence for a quasistatic process (), it follows .

First we consider constant volume, whence

hence .

Now consider constant pressure, whence

whence .

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