Chemistry - Thermodynamics - I Question with Solution | TestHub
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 same final volume, which is double the original volume thereby causing the 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:(select one or more)
Answer:
Solution:
With vibrations active, Cv,m = Ne 1.5R; O2 3.5R; SO2 (nonlinear, 3 vibrations) 6R; CH4 (9 vibrations) 12R. Step I: T2 = T1 2-R/Cv, so the fall T1(1 - 2-R/Cv) is largest for the smallest Cv, i.e. Ne: (a) true. Step II heat per mole = Cv T1(1 - 2-R/Cv)/R in units of RT1: Ne 0.555, O2 0.629, SO2 0.655, CH4 0.673, so largest for CH4: (b) true. Initial and final T are equal for an ideal gas, so Δ U = 0: (c) true. Both gases reach the same end state but the adiabat of Step I follows different γ, so the P-V paths differ: (d) false. Ans: (a), (b), (c).
