Solution 43E

Step 1

If the temperature of a gas is , then the energy per degrees of freedom is given by

Where  is the boltzmann’s constant. Since Nitrogen (N2) is a diatomic molecule, the degrees of freedom of nitrogen molecule is 5. Hence the energy per molecule is

Now in one mole of N2 there will be  number of molecules, hence the total energy of the gas is

Now, suppose , heat is supplied to the system. Since the process is constant volume process, there will be no work done. Hence, so all energy will be used to change in temperature, hence the change in temperature is given by

 So the molar specific heat at constant volume is

Now, the molar mass of N2 is . Hence the specific at constant volume is given by

Now we know that the specific heat of water is

Which is much greater than the specific heat of nitrogen at constant volume.