Question

In a flexible balloon, $2$ moles of $S{O}_2$ having initial volume of $1kl$ at a temperature of $27{}^{o}C$ is filled ($S{O}_2$ is a non linear triatomic gas). The gas is first expanded to thrice its initial volume isobarically and then expanded adiabatically so as to attain its initial temperature. Assuming gas is ideal and $R=\frac{25}{3}Jmo{l}^{-1}{K}^{-1}$. Choose the incorrect options.

• A. Change in internal energy of the gas in the isobaric process is $2.5\times {10}^{4}J$
• B. Change in internal energy of the gas in the isobaric process is $3\times {10}^{4}J$
• C. Work done by the gas in the whole process is $35kJ$
• D. Work done by the gas in the whole process is $40kJ$

Answer 1

Answer: (A), (C)

The correct options are
A Change in internal energy of the gas in the isobaric process is $2.5\times {10}^{4}J$
C Work done by the gas in the whole process is $35kJ$

The V-T diagram for the process would be
Since AB is an isobaric process, from ideal gas equation
$V\propto T$
$\therefore \frac{V_A}{T_A}=\frac{V_B}{T_B}$
$\Rightarrow \frac{1}{300}=\frac{3}{T_B}$
$\Rightarrow T_B=900K$
Change in internal energy for process AB,
$dU=n{C}_{v}dt$
For non linear triatomic gas, $C_v=\frac{6R}{2}$
$\therefore dU=2\times \left(\frac{6R}{2}\right)(900-300)$
$dU=3\times {10}^{4}J$


Work done by the gas in whole process,
$W=W_{ab}+W_{bc}$
For isobaric process AB, work done $W_{ab}=PdV=nRdT=2\times \frac{25}{3}\times (900-300)=10kJ$
For adiabatic process BC, work done
$W_{bc}=\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}=\frac{nRdT}{\gamma -1}$
For a non-linear triatomic gas, degree of freedom$\left(f\right)$ is 6
Thus, $\gamma =1+\frac{2}{f}=1+\frac{1}{3}=\frac{4}{3}$
$\therefore W_{bc}=\frac{nRdT}{\gamma -1}=\frac{2\times \frac{25}{3}\times 600}{\frac{4}{3}-1}=30kJ$
Total work done, $W=10+30=40kJ$