Chemistry - Thermodynamics - I Question with Solution | TestHub

Question Explanation:

Calculate the work performed by diatomic gas given the increase in internal energy.

Concept:

Work, Heat, and $\Delta$ U relation in the process

Solution:

${\mathrm{C}}_{\mathrm{V}}=\frac{3}{2}\mathrm{R}+2\times \frac{1}{2}\mathrm{R}=\frac{5}{2}\mathrm{R}$

$\Delta \mathrm{U}=\alpha \left(\sqrt{{\mathrm{V}}_2}-\sqrt{{\mathrm{V}}_1}\right)=100$

$\mathrm{W}=2(\alpha )(\gamma -1)\left(\sqrt{{\mathrm{V}}_2}-\sqrt{{\mathrm{V}}_1}\right)=(2)(\gamma -1)\times 100$

$\gamma =\frac{7}{5}\gamma -1=\frac{2}{5}$

$\mathrm{W}=2\times \frac{2}{5}\times 100$

$\mathrm{W}=80\mathrm{J}$ Final Answer: Option (A)