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  4. 2 mole of an ideal gas at 27°C temperature is expanded reversibly from 2 lit to 20 lit. Find the entropy change (R = 2 cal/mol K) :-

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Q. 2 mole of an ideal gas at $27^{\circ}C$ temperature is expanded reversibly from 2 lit to 20 lit. Find the entropy change (R = 2 cal/mol K) :-

AIPMTAIPMT 2002Thermodynamics

Solution:

for isothermal reversible expansion
$w = q = nRT \times 2.303 \, \log \frac{v_2}{v_1}$
$ = 2RT \times 2.303 \, \log \frac{20}{2}$
$ = 2 \times 2 \times T \times 2.303 \times 1 = 9.2 T$
Entropy change, $\Delta S = \frac{q}{T} = \frac{9.2T}{T} = 9.2$ cal .