Question

One mole of an ideal monoatomic gas expands isothermally against constant external pressure of 1 atm from initial volume of 1L to a state where its final pressure becomes equal to external pressure. If initial temperature of gas is 300 K then total entropy change of system in the above process is :
($R=0.082Latm{mol}^{-1}{K}^{-1}=8.3{mol}^{-1}{K}^{-1}$)

• A. 0
• B. $R\ell n\left(24.6\right)$
• C. $R\ell n\left(2490\right)$
• D. $\frac{3}{2}R\ell n\left(24.6\right)$

Answer 1

Answer: (B)

$R\ell n\left(24.6\right)$

Initial pressure, $P=\frac{RT}{V}$

$P=300\times R=300\times 0.0821$ atm.

Final pressure $1$ atm

Final volume ;

$P_f{V}_f=P_i{V}_i$

$V_f=\frac{P_i{V}_i}{P_f}=\left(\frac{300\times R}{1}\right)=24.63L$

Now,

$\Delta S=nR\ln \frac{V_2}{V_1}$

$\Delta S=R\ln \left(\frac{24.6}{1}\right)$