A thermally insulated vessel contains an ideal gas of molar mass M . The vessel is moving with a constant speed v and is suddenly brought to rest. If the temperature of the gas is observed to increase by T , the molar heat capacity at constant pressure, C_p , of the gas is : ( R is the universal gas constant)

Step-by-step solution

Let n be the number of moles of the gas in the vessel. The total mass of the gas is n M . The macroscopic kinetic energy of the gas before the vessel stops is K = 1 2 (nM)v^2 . Since the vessel is thermally insulated, the loss in macroscopic kinetic energy is entirely converted into the internal energy of the gas. U = K n C_v T = 1 2 n M v^2 Solving for the molar heat capacity at constant volume, C_v : C_v = M v^2 2 T Using Mayer's relation, C_p - C_v = R , we get the molar heat capacity at constant pressure : C_p