 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2017/paper-2/section-c/c11/b/solution

H = U + p V

p V = RT + p b

, so

H = C_{V} T + U_{*} + RT + p b .

At fixed pressure,

p b

is constant. Therefore

C_{p} = (\frac{\partial H}{\partial T})_{p} = C_{V} + R, γ = \frac{C _{p}}{C _{V}} = 1 + \frac{R}{C _{V}} .

Since

C_{V}

and

R

are constants, this ratio is independent of both temperature and pressure. Although the gas is not mechanically ideal when

b \neq = 0

R

in this model.

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