Assume ideal gas behaviour for all the gases considered and vibrational degrees of freedom to be act — Thermodynamics and Thermochemistry Chemistry Question
Question
Assume ideal gas behaviour for all the gases considered and vibrational degrees of freedom to be active. Separate equimolar samples of Ne, $\text{O}_2$, $\text{SO}_2$ and $\text{CH}_4$ gases were subjected to a two-step process as mentioned. Initially all are at the same temperature and pressure.<br>Step I: All undergo reversible adiabatic expansion to attain same final volume, which is double the original volume thereby causing the decrease in their temperature.<br>Step II: After Step I, all are given appropriate amount of heat isochorically to restore the original temperature.<br>Which of the following is/are correct statement(s)?
💡 Solution & Explanation
Step I (adiabatic expansion): $T_2/T_1 = (V_1/V_2)^{\gamma-1}$. Neon has the highest $\gamma$ (monoatomic, 5/3), causing the steepest temperature drop. By Step II, restoring the exact initial temperature for an ideal gas strictly resets the internal energy to its initial value, yielding zero net change ($\Delta U_{total} = 0$).