Past exam of the physics B course of the University of Cambridge / 2017 / Paper 2 / Section C / C11 / b

Table of contents
- Solution b

Solution

Use the enthalpy

H = U + p V

. The equation of state gives

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

, its constant-pressure/constant-volume heat-capacity difference remains

R

in this model.

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