Of nitrogen, treated as a diatomic ideal gas with , is held in a cylinder closed by a…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Thermal, Statistical & Complex Systems · Calculus of change and accumulation

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

Problem

n = 0.500\ \mathrm{mol}

of nitrogen, treated as a diatomic ideal gas with

C_V = \tfrac52 nR

, is held in a cylinder closed by a frictionless piston. The cylinder sits in a large bath at

T = 295\ \mathrm{K}

, and the gas is expanded quasistatically and isothermally from

3.00\ \mathrm{L}

9.00\ \mathrm{L}

. Write

Nk_B = nR

. Chapter 3's convention

\Delta U = Q + W

is used, with

W

the work done on the gas. ((a)) Show that

\delta Q = \tfrac52 nR\,\mathrm{d}T + \dfrac{nRT}{V}\,\mathrm{d}V

, the heat delivered to this gas in a quasistatic step, is not an exact differential in

T

and

V

, and say what that means for the phrase "the heat content of the gas". ((b)) Find

\Delta F

for the gas in this expansion. ((c)) Find the work the gas delivers, and state why it reaches the bound set by

\Delta F

. ((d)) Find the entropy change of the bath.

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