Chemistry - Thermodynamics - I Question with Solution | TestHub
Four samples A, B, C and D of the same ideal gas (γ = 1.5) have equal volumes and temperatures. The volume of each sample is made four times. The process is isothermal for A, reversible adiabatic for B, isobaric for C, and for D an irreversible adiabatic expansion against a constant external pressure equal to the final pressure. If the final pressures are equal for all four samples, then the ratio of their initial pressures PA : PB : PC : PD is
Options:
Answer:
Solution:
Let the final pressure be Pf and the initial volume V (final 4V). A: PAV = Pf · 4V, so PA = 4Pf. B: PB = 41.5Pf = 8Pf. C: PC = Pf. D: CV = R/(γ - 1) = 2R, so Δ U = (CV)/R(Pf · 4V - PDV) = 2(4Pf - PD)V and W = -Pf(3V). Setting Δ U = W: 8Pf - 2PD = -3Pf, so PD = 5.5Pf. Ratio 4 : 8 : 1 : 5.5 = 8 : 16 : 2 : 11. Matches (d).
