# Specific Heat Capacity

Whenever heat is supplied to a solid (or liquid), its temperature rises. If the same amount of heat is supplied to the same mass of different solids, the rise in temperature will be different for the different solids. In other words, the rise in temperature produced, when a certain amount of heat is supplied to a solid, depends upon the nature of the solid. This nature of the solid is characterized by the term specific heat capacity or simply the specific heat of the solid.

The specific heat of a solid (or a liquid) may be defined as the amount of heat required to raise the temperature of the unit mass of the solid (or the liquid) through 10 C. It is denoted by C.

In S.I., the specific heat of a solid (or liquid) may be defined as the amount of heat required to raise the temperature of 1 kg of the solid (or liquid) through 1K (or 10C).

The unit of specific heat is J kg-1 K-1 and SI and cal g-1 C-1 in cgs system.

If an amount of heat Î”Q is needed to raise the temperature of mass M of the solid through Î”T then from the definition of specific heat, we have
C =

The above equation may be written asÎ”Q = m C Î”T

The molar specific heat of the material of a solid (or liquid) is defined as the amount of heat required to raise the temperature of one mole of solid (or liquid) through 1K (or 10C). It is denoted by C. Its unit is J mol-1K-1

Therefore the amount of heat required to raise the temperature of Î¼ moles of a solid through Î”T is given by
Î”Q = Î¼ C Î”T
1. When a solid is heated through a small range of temperature, its volume remains more or less constant. Therefore, specific heat of a solid may be called as specific heat at constant volume and may also be denoted by Cv.
2. When a solid is heated through a small range of temperature, its pressure remains more or less constant. Therefore, specific heat of a solid may be called as specific heat at constant pressure and may also be denoted by CP
3. When heat is supplied to a gas, its volume and pressure change in temperature and likewise the amount of heat required to raise the temperature of 1 gm of a gas through 10C will posses a value depending upon the manner, it is heated.
Since, gas may be heated under a numerous set the values of P and V; its specific heat can possess infinite number of values. In other words, unless a gas is supplied heat under specified conditions, its specific heat will not have a unique value. So that the specific heat of a gas may have a definite meaning, the specific heat of a gas is either measured at a constant volume or at a constant pressure.