(a) Calculate the specific heat at constant volume of

Solution 44E Step 1 The thermal energy per degrees of freedom is given by 1 E 1 k 2 B So if there are f degrees of freedom per molecule, then the energy per molecule is given by f E 2 k T B 2 Now if there are N number of molecule in the gas, then the total thermal energy is given by E = Nk T 2 B From the above equation we can write that f E = Nk2T B Now, the number of molecule per mole is given by N = 6.02 × 10 23/mol As stated in the problem, the number of degrees of freedom for the water molecule is f = 3 + 3 = 6 Hence the molar specific heat at constant volume will be for water vapor will be c = E = Nk = (6.02 × 10 )(1.38 × 10 23 J/mol.K) = 24.9 J/mol v T 2 B 2 3 Now the molar mass of water is M = 18.0 g/mol = 18.0 × 10 kg/mol So the specific heat at constant volume of the water vapor is C = cv= 24.93/mol = 1385 J/kg V M 18.0×10 kg/mol