Question

Assume ideal gas behaviour for all the gases considered & neglect vibrational degrees of freedom. Separate equimolar sample of $Ne,O_2,C{O}_2$ & $S{O}_2$ were subjected to a two-step process as mentioned. Initially, all are at the same state of temperature & pressure.
Step- I $\to$ All undergoes reversible adiabatic expansion to attain same final volume, which is double the original volume thereby causing the decreases in their temperature.
Step- II $\to$ After step-I all are given an appropriate amount of heat at a constant volume to restore the original temperature.
Mark the correct option(s).

• A. Due to step-I only, the decrease in temperature will maximum for $Ne$
• B. During step-II, heat given will be minimum for $S{O}_2$
• C. There will be no change in internal energy for any of the gas after both the steps of process are completed
• D. The $P-V$ graph of $O_2$ & $C{O}_2$ will be same

Answer 1

Answer: (A), (C), (D)

The correct options are
A Due to step-I only, the decrease in temperature will maximum for $Ne$
C There will be no change in internal energy for any of the gas after both the steps of process are completed
D The $P-V$ graph of $O_2$ & $C{O}_2$ will be same

As internal energy is only temperature dependent and initial and final temperature are same so there will be no change in internal energy for any of the gas after both the steps of a process are completed.
Also,
$C_v=\frac{R}{\gamma -1}$ and $\gamma$ is maximum for $Ne$, so due to step-I only, the decrease in temperature will maximum for $Ne$.