 # Why cp is greater than cv?

Cp = Molar heat capacity at constant pressure

Cv = Molar heat capacity at constant volume

When a gas is heated at a constant volume, the work done on the gas increases the internal energy of the system. At constant pressure, when a gas is heated, work is done to overcome the pressure and there is an expansion in the volume with an increase in the internal energy of the system. Therefore, it can be said that Cp is greater than Cv.

• If we had a means of measuring the quantity of heat that is imparted to the gas, we would observe that the heat capacity CP is greater than CV.
• The difference is due to the fact that in the first case, the gas changes its volume (expands).
• Cp is greater than the molar specific heat at constant volume Cv because energy must now be supplied not only to raise the temperature of the gas but also for the gas to do work.
• At constant pressure, a part of the heat absorbed is utilized in performing external work while at a constant volume all the heat is utilized in increasing the internal energy of the system.
• It follows therefore that the temperature rise at constant pressure will be less for a given quantity of heat transferred.
• More heat would be required at constant pressure to cause the same temperature rise and Cp will be greater than Cv. (24) (0)