Question

Pressure of 10 moles of an ideal gas is changed from 2 atm to 1 atm against constant external pressure without change in temperature. If surrounding temperature (300 K) and pressure (1 atm) always remains constant then calculate total entropy change ($\Delta S_{system}+\Delta S_{surrounding})$ for given process. [Given: ℓn2 = 0.70 amd R=8.0 J/mol/K]

• A. 56 J/K
• B. 14 J/K
• C. 16 J/K
• D. None of these

Answer 1

The correct option is C

16 J/K

$\Delta S_{system}=nRln\frac{p_1}{p_2}=10\times 8ln\frac{2}{1}=56J/K$

$\Delta S_{surrounding}=-\frac{q}{T}$

$\Delta U=q+w,-w=P_{ext}(V_2-V_1)$

$q-P_{ext}(\frac{nRT}{p_2}-\frac{nRT}{p_1})=nRT(\frac{P_{ext}}{p_2}-\frac{P_{ext}}{p_1})$

= $10\times 8\times T(1-\frac{1}{2})$

$\Delta S_{surrounding}=-\frac{-q}{T}\Rightarrow -40J$;

$\Delta S_{system}+\Delta S_{surr}=56-40\Rightarrow 16J/K$