(a) For the form , with and independent variables, and , evaluate and state whether…

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Thermodynamic potentials and the formal structure of thermodynamics

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

Problem

(a) For the form

M\,\mathrm{d}x+N\,\mathrm{d}y

, with

x

and

y

independent variables,

M=2y

and

N=3x

, evaluate

(\partial M/\partial y)_x-(\partial N/\partial x)_y

and state whether the form is exact. (b) Write the differential of the enthalpy

H

in its natural variables and read off

(\partial H/\partial p)_S

. (c) A cylinder holds

N=1.20\times10^{23}

molecules of an ideal gas in thermal contact with a reservoir at

T=290\,\mathrm{K}

, so the temperature stays fixed. The gas is compressed from

V_1=4.00\,\mathrm{L}

V_2=1.00\,\mathrm{L}

. Find

\Delta F

for the gas and the least work that must be done on it.

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