Three samples of the same gas A, B and $C (γ = 3 / 2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for A, isobaric for B and isothermal for C. If the final pressures are equal for all the three samples, the ratio of their initial pressures is:

2 \sqrt{2} : 2 : 1

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2 \sqrt{2} : 1 : 2

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\sqrt{2} : 1 : 2

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2 : 1 : \sqrt{2}

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Solution

The correct option is B $2 \sqrt{2} : 1 : 2$
For isobaric process, pressure will remain same $P_{B} = P$ .
For isothermal proces, $P_{1} V_{1} = P_{2} V_{2} \Rightarrow P_{C} \times V = P \times 2 V$
So $P_{C} = 2 P$
For adiabatic process, $P V^{γ} \Rightarrow P_{A} V^{1.5} = P (2 V)^{1.5}$
$P_{A} = 2 \sqrt{2} P$
Therefore $P_{A} : P_{B} : P_{C} = 2 \sqrt{2} : 1 : 2$

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Three samples of the same gas A, B and $C (γ = 3 / 2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for A, isobaric for B and isothermal for C. If the final pressures are equal for all the three samples, the ratio of their initial pressures is: