ThermodynamicsHard
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
Options
A.1: 1: 1
B.2: 2: 1
C.2: 2$\sqrt{2}$: 1
D.1: 2$\sqrt{2}$: 2
Solution
Isothermal: $P_{A}.V = P.(2V) \Rightarrow P_{A} = 2P$
Adiabatic: $P_{B}.V^{1.5} = P.(2V)^{1.5} \Rightarrow P_{A} = 2\sqrt{2}P$
Isobaric: PC = P
∴ PA: PB: PC = 2: 2 2: 1
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