(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>0

and

y

independent variables,

M=y/x

and

N=\ln x

, evaluate

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

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

U

in its natural variables and read off

(\partial U/\partial S)_V

. (c)

N=1.00\times10^{23}

molecules of an ideal gas expand at the fixed temperature

T=300\,\mathrm{K}

, held there by a reservoir, and deliver the greatest work that this change allows, namely

500\,\mathrm{J}

. By what factor

V_2/V_1

did the volume increase?

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