Three samples A , B and C of the same gas ( γ = 1.5 ) initially have equal volumes and temperatures. Each sample's volume is doubled, with the process being isothermal for A , adiabatic for B , and isobaric for C . If

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Quantrex Academy · Accepted Answer

Correct answer: B. 2 : 2 2 : 1

Let the initial volume of each sample be

V_0

and the final pressure of each sample be

P_f

.

For sample

A

(isothermal process):

P_A V_0 = P_f (2V_0) \Rightarrow P_A = 2P_f

For sample

B

(adiabatic process):

P_B V_0^{\gamma} = P_f (2V_0)^{\gamma}

Given

\gamma = 1.5 = \dfrac{3}{2}

,

P_B = P_f (2)^{3/2} = 2\sqrt{2}P_f

For sample

C

(isobaric process):
Pressure remains constant, so

P_C = P_f

The ratio of their initial pressures is:

P_A : P_B : P_C = 2P_f : 2\sqrt{2}P_f : P_f = 2 : 2\sqrt{2} : 1

Three samples A , B and C of the same gas ( γ = 1.5 ) initially...

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