Carbon dioxide is modelled by the pressure law used in the text

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Interacting systems, real gases and phase equilibria

Thermal Physics, Ch Thermodynamic potentials, Legendre transforms and Maxwell relations

Problem

Carbon dioxide is modelled by the pressure law used in the text, written per mole,

p = \frac{nRT}{V - nb_{\rm ex}} - \frac{a_{\rm att}n^{2}}{V^{2}},

with

n

the number of moles,

R = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}

a_{\rm att} = 0.364\,\mathrm{Pa\,m^{6}\,mol^{-2}}

and

b_{\rm ex}

a constant whose value is not needed below. A sample of

n = 2.00\,\mathrm{mol}

is held at the fixed temperature

T = 300\,\mathrm{K}

and expands quasistatically from

V_1 = 4.00\,\mathrm{L}

V_2 = 20.0\,\mathrm{L}

(

1\,\mathrm{L} = 10^{-3}\,\mathrm{m^{3}}

). ((a)) Show, using the energy equation of a gas, that

(\partial U/\partial V)_{T} = a_{\rm att}n^{2}/V^{2}

for this gas. ((b)) Evaluate

(\partial U/\partial V)_{T}

in the initial state. ((c)) Find the change

\Delta U

of the internal energy in the expansion.

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