ThermodynamicsHard

Question

Assume ideal gas behaviour for all the gases considered and vibrational degrees of freedom to be active. Separate equimolar samples of Ne, O2, SO2 and CH4 gases were subjected to a two-step process as mentioned. Initially, all are at the same temperature and pressure.

Step I: All undergo reversible adiabatic expansion to attain the same final volume, which is double the original volume thereby causing decrease in their temperature.

Step II: After Step I, all are given appropriate amount of heat isochorically to restore the original temperature. Which of the following is/are correct statement(s)?

Options

A.Due to Step I only, the decrease in temperature will be maximum for Ne.
B.During Step II, heat given will be maximum for CH4.
C.There will be no change in internal energy for any gas after both the steps of process are completed.
D.The P–V graph of CH4 and SO2 will be the same for overall process.

Solution

Here, $\gamma$decreases on increasing degree of freedoms. As final pressure is minimum for Ne, its final temperature is minimum (decrease in temperature is maximum).

Now, for overall process, $\Delta T = 0 \Rightarrow \Delta U_{\text{total}} = 0$

Or, $\Delta U_{I} + \Delta U_{II} = 0 \Rightarrow \left( 0 + w_{I} \right) + \left( q_{II} + 0 \right) = 0$

$\therefore q_{II} = - w_{I} =$maximum for CH4

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