Answer
See the detailed answer below.
Work Step by Step
We know that the molar-specific heat of a gas is the amount of heat energy required to raise the temperature of one mole of the gas by one degree Celsius.
The molar specific heat at constant pressure $C_{\rm p}$ is larger than the molar specific heat at constant volume $C_{\rm v}$ because, at constant pressure, some of the added heat energy is used to do work on the surroundings to increase the volume of the gas, in addition to increasing the internal energy and temperature of the gas.
This means that more heat energy is needed to achieve the same temperature increase when the gas pressure is constant, compared to the needed energy when the gas is at a constant volume.
We know that the difference between $C_{\rm p}$ and $C_{\rm v}$ can be expressed using the gas constant $R$ where
$$C_{\rm p}- C_{\rm v}=R$$
where $R$ is a constant value for an ideal gas.
Hence $C_{\rm p}$ is always greater than $C_{\rm v}$ for any ideal gas.
