A fixed sample of argon (a monatomic ideal gas with constant heat capacities, ) is…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Temperature, heat and the macroscopic behaviour of matter · The laws of thermodynamics

Thermal Physics, Ch The first law: work, heat and internal energy

Problem

A fixed sample of argon (a monatomic ideal gas with constant heat capacities,

\gamma = 5/3

) is taken quasistatically round the following closed three-leg path. State A is

V_A = 3.00\,\mathrm{L}

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

T_A = 300\,\mathrm{K}

. A

\to

B: isothermal compression at

300\,\mathrm{K}

V_B = 1.00\,\mathrm{L}

, the cylinder in a large water bath. B

\to

C: the bath is removed and the cylinder perfectly lagged; the gas expands quasistatically and adiabatically back to

V_C = 3.00\,\mathrm{L}

. C

\to

A: the volume is held at

3.00\,\mathrm{L}

and the gas is warmed back to

300\,\mathrm{K}

. Use

\Delta U = Q + W

with

W

the work done on the gas and

\delta W = -p\,\mathrm{d}V

. ((a)) Find

Nk_B

for the sample. ((b)) Find the temperature at C. ((c)) Find

W

and

Q

for each of the three legs, in the order A

\to

B, B

\to

C, C

\to

A. ((d)) Find the net work done on the gas and the net heat delivered round the whole path, and check them against

\Delta U

for the loop.

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