# 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 1

^{0 }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 1

^{0}C).

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 1

^{0}C). It is denoted by C. Its unit is J mol

^{-1}K

^{-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**

- 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
**C**._{v} - 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
**C**_{P} - 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 1
^{0}C will posses a value depending upon the manner, it is heated.