Final answer:
The relationship between the molar heat capacities at constant pressure (Cp) and constant volume (Cv) in thermodynamics is Cp = Cv + R, which is approximately valid for all dilute gases.
Step-by-step explanation:
In thermodynamics, the relationship between the molar heat capacity at constant pressure (Cp) and the molar heat capacity at constant volume (Cv) is derived using the ideal gas law and is given by Cp = Cv + R, where R is the ideal gas constant. This relationship is approximately valid for all dilute gases, which can be monatomic, diatomic, or polyatomic in nature. The derivation is based on energy changes in a system during constant volume and constant pressure processes under the framework of the first law of thermodynamics.
For an ideal gas, Cp is greater than Cv because when a gas is heated at constant pressure, it does some work in expanding against the external pressure, thus requiring more heat energy than if it were heated in a constant volume condition where no work is done.