Question

Why specific heat of a gas at constant pressure is always greater than the specific heat of a gas at constant volume?

Answer 1

$C_P>C_V$
$C_P$ is greater than $C_V$ because when a gas is heated at constant volume, no external work is done and so the heat supplied is consumed only in increasing the internal energy of a gas.
But if the gas is heated at constant pressure, the gas expands against the external pressure so does some external work. in this case the heat is used up in increasing the internal energy of the gas and in doing some external work.
Since the internal energy depends only on temperature, for the same rise of temperature the internal energy of a mass of a gas will increase by the same amount whether the pressure or volume remains constant. But since external work is additionally done for constant pressure than at constant volume to produce the same rise in temperature of the gas.
Above is the reason why $C_P$ is greater than $C_V$.