# Specific Heats of a Gas

The specific heat of a substance may be broadly defined as the amount of heat required to raise the temperature of its unit mass through 1°. All the liquids and solids have one specific heat only. But a gas can have any number of specific heats (lying between zero and infinity) depending upon the conditions, under which it is heated.

Following are the two types of specific heats of a gas :

1. Specific heat at constant volume. It is the amount of heat required to raise the temperature of a unit mass of gas through 1°, when it is heated at a constant volume. It is generally denoted by Cv

Let
m = Mass of the gas,
T1 = Initial temperature of the gas, and
T2 = Final temperature of the gas.

Total heat supplied to the gas at constant volume,
Q = Mass x Sp.heat at constant volume x Rise in temperature
Q = m.Cv(T2—T1)

A little consideration will show, that whenever a gas is heated at constant volume, no work is done by the gas. The whole heat energy is utilized in increasing the temperature and pressure of the gas. In other words, all the amount of heat supplied remains within the body of the gas, and represents the increase in internal energy of the gas.

Note: When the specific heat at constant volume (Cv) is multiplied by the molecular mass of a gas (M), it is called volumetric or molar specific heat at constant volume. It is denoted by Cvm. Mathematically,

Cvm = M.Cv

2. Specific heat at constant pressure. It is the amount of heat required to raise the temperature of a unit mass of a gas through 1°, when it is heated at constant pressure. It is generally denoted by Cp.

Let
m = Mass of the gas,
T1 = Initial temperature of the gas,
v1 = Initial volume of.the gas, and
T2, v2 = Corresponding values for the final conditions of the gas.

Total heat supplied to the gas at constant pressure,

Q = Mass x Sp. heat at constant pressure x Rise in temperature

Q = m.Cp(T2-T1)

Whenever a gas is heated at a constant pressure, the heat supplied to the gas is utilised for the following two purposes :

1. To raise the temperature of the gas. This heat remains within the body of the gas, and represents the increase in internal energy. Mathematically, increase in internal energy,

dU = m.Cv (T2– T1)

2. To do some external work during expansion. Mathematically, workdone by the gas,

W = p (v2– v1) = m.R (T2– T1)

It is thus obvious, that the specific heat at constant pressure is higher than the specific heat at constant volume.

Note: When the specific heat at constant pressure (Cp) is multiplied by the molecular mass of a gas (M), it is called volumetric or molar specific heat at constant pressure. It is denoted by Cpm. Mathematically,

Cpm = M.Cp