Question

Two moles of ideal monoatomic gas was taken through isochoric heating from 100 K to 800 K. If the process is carried out irreversibly (one step) then $\Delta S_{system}+\Delta S_{surrounding}$ is

[Given : $ln2=0.7$ and $R=2cal/molK$]

• A. 0
• B. 3.675 cal/K
• C. 7.35 cal/K
• D. None of these

Answer 1

The correct option is C

7.35 cal/K

$\Delta S_{system}=n{C}_{v,m}ln\left(\frac{T_2}{T_1}\right)\Rightarrow 2\times \frac{3}{2}Rln\left(\frac{800}{100}\right)$

$\Delta S_{system}=3Rln8=12.6cal/K$

Entropy of surrounding = $-q/T$
$q=n{C}_v\Delta T$

$\Delta S_{surrounding}=-\frac{2\times \frac{3}{2}R\times 700}{800}\Rightarrow -2.625R$

$\Rightarrow -5.25cal/K$

$\Delta S_{total}=7.35cal/K$