A Carnot engine uses atoms of helium

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

Thermal Physics, Ch Heat engines, refrigerators and the Carnot cycle

Problem

A Carnot engine uses

N = 2.00\times10^{22}

atoms of helium, treated as an ideal monatomic gas with

C_V = \tfrac32 Nk_B

and

\gamma = 5/3

, between reservoirs at

450\,\mathrm{K}

and

280\,\mathrm{K}

. The isothermal expansion at

450\,\mathrm{K}

triples the volume. All four legs are quasistatic and frictionless, and heat crosses only between bodies at the same temperature. Take

k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}

, and use

\Delta U = Q + W

with

W

the work done on the gas. ((a)) Find the heat

Q_h

absorbed on the hot isotherm. ((b)) Find the work done on the gas during the adiabatic expansion from

450\,\mathrm{K}

280\,\mathrm{K}

. ((c)) Show that the two adiabatic legs contribute no net work to the cycle, and find the net work delivered per cycle. ((d)) Find the efficiency, once from the two heats and once from the two temperatures.

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