A cylinder closed by a frictionless piston of negligible mass contains of nitrogen

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · The laws of thermodynamics

Thermal Physics, Ch The second law, entropy and irreversibility

Problem

A cylinder closed by a frictionless piston of negligible mass contains

2.00\,\mathrm{mol}

of nitrogen, treated as an ideal gas with constant heat capacities. The gas starts at

350\,\mathrm{K}

and

300\,\mathrm{kPa}

. The cylinder walls conduct heat and the cylinder stands in a large bath of water at

350\,\mathrm{K}

, big enough that its temperature does not change during the process. The piston is released and the gas pushes it outwards against a constant external pressure of

100\,\mathrm{kPa}

until the gas comes to rest in equilibrium at

100\,\mathrm{kPa}

and

350\,\mathrm{K}

. Use

\Delta U = Q + W

with

W

the work done on the gas, and

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

. ((a)) Find the heat delivered to the gas by the bath. ((b)) Find

\Delta S

of the gas. ((c)) Find

\Delta S

of the bath. ((d)) Find the total entropy change. ((e)) Find the lost work, taking the bath at

350\,\mathrm{K}

as the coldest body available, and check it against the work a reversible isothermal expansion between the same end states would have delivered.

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