Three samples A, B and C of the same ideal gas () have equal volumes and temperatures. The volume of — Thermodynamics and Thermochemistry Chemistry Question
Question
Three samples A, B and C of the same ideal gas ($\gamma = 1.5$) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressures are equal for the three samples, then the ratio of their initial pressures is
Answer: C
💡 Solution & Explanation
Set final pressure to $P_f$. A (Iso): $P_A V = P_f (2V) \implies P_A = 2P_f$. B (Adia): $P_B V^{1.5} = P_f (2V)^{1.5} \implies P_B = 2^{1.5}P_f = 2\sqrt{2}P_f$. C (Isobaric): $P_C = P_f$. The resulting ratio is $2 : 2\sqrt{2} : 1$.
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