Define specific heat capacity.

1. (a)Define specific heat capacity.[2]
2. (b)(i)A sealed container of fixed volume V contains N molecules, each of mass m, of an ideal gas at pressure p. State an expression, in terms of V, N, p and the Boltzmann constant k, for the thermodynamic temperature T of the gas.[1]
3. (b)(ii)Show that the mean translational kinetic energy E_K of a molecule of the gas is given by E_K = (3/2)kT.[2]
4. (b)(iii)Explain why the internal energy of the gas is equal to the total kinetic energy of the molecules.[2]
5. (c)(i)The gas in (b) is supplied with thermal energy Q. Explain, with reference to the first law of thermodynamics, why the increase in internal energy of the gas is Q.[2]
6. (c)(ii)Use the expression in (b)(ii) and the information in (c)(i) to show that the specific heat capacity c of the gas is given by c = 3k / 2m.[2]
7. (d)The container in (b) is now replaced with one that does not have a fixed volume. Instead, the gas is able to expand, so that the pressure of the gas remains constant as thermal energy is supplied. Suggest, with a reason, how the specific heat capacity of the gas would now compare with the value in (c)(ii).[2]