Question

Assume ideal gas behaviour for all gases and neglect vibrational degrees of freedom. Separate equimolar samples of $Ne,O_2,C{O}_2$ and $S{O}_2$ were subjected to the two processes as mentioned below. Initially, all are at the same rate of temperature and pressure.
Step I $\to$ All undergo reversible adiabatic expansion to attain the 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 appropriate amount of heat isochorically to restore the original temperature.
Now, mark the correct option(s).

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

Answer 1

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

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

As $\gamma$ is maximum for $Ne$, so from step I the decrease in temperature will be maximum for $Ne$.
The $P-V$ graph of $O_2$ and ${CO}_2$ will be the same as their degrees of freedom are the same (neglect vibrational degrees of freedom).
There will be no change in internal energy for any of the gases after both the steps of the process are completed as internal energy is a state function and it is temperature dependent only.