Specific heat of a gas

Specific heat of a gas 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 specific heats depending upon mission under which it is heated.

Following are the two types of specific heat 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 constant volume. It is generally donated by CV
Let,.     m = mass of the gas
T1  = initial temperature of the gas
T2 = final temperature of the gas

Total heat supplied to the gas at constant volume,

Q = mass x Sp. At constant volume x rise temperature
= m.cv (T1 – T2)

A little consideration will show that whenever a gas is heated at constant volume no work is donated 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 X the molecular mass of gas (M), it is called volumetric or molar specific heat at constant volume. It is denoted by Cvm
Mathematical expression,
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
T2 , v2 = corresponding values for the final condition of the gas.

Total heat supplied to the gas as constant pressure,…
Q = mass x Sp. Heat at constant pressure x rise in temperature.
= m.cp (T1 – T2)
Whenever a gas is heated at a constant pressure the heat supplied to the gas is utilized for the following to purpose.

a) to rise the temperature of the gas. This heat remains within the body of the gas and represents the increase in initial energy,

dU = m.cv (T1 – T2)

b) to do some external work during expansion.

W = p( v1 – v2) = m.R (T1 – T2)
It is thus obvious that the Pacific heat at constant pressure is higher than the Pacific heat at constant volume.

Cpm = M.cp

Note- when the Pacific heat at constant pressure (CP) is X the molecular mass of the gas (M), it is called volumetric for molar specific heat at constant pressure.