The barrel of a bicycle pump holds of air at and

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

The barrel of a bicycle pump holds

3.00\times10^{-4}\,\mathrm{m^3}

of air at

1.00\times10^{5}\,\mathrm{Pa}

and

290\,\mathrm{K}

. The outlet is blocked and the air is compressed quasistatically and adiabatically to one fifth of its volume, with no friction at the piston. Treat the air as an ideal diatomic gas with constant heat capacities,

C_V = \tfrac52 Nk_B

and

\gamma = 7/5

. Use

\Delta U = Q + W

with

W

the work done on the gas, and

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

. ((a)) Find the temperature of the air at the end of the compression. ((b)) Find the work done on the air during the compression. ((c)) This compression is now used as the adiabatic compression leg of a Carnot cycle running between

290\,\mathrm{K}

and the temperature found in (a). Find the efficiency of that cycle. ((d)) In the cycle, the isothermal expansion at the hot temperature takes the gas from

6.00\times10^{-5}\,\mathrm{m^3}

1.20\times10^{-4}\,\mathrm{m^3}

. Find the heat taken in on that leg and the net work delivered per cycle.

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