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Three samples of the same gas A, B and C $γ = \frac{3}{2}$ 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 three samples, the ratio of their initial pressures are

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2 \sqrt{2} : 2 : 1

$2 \sqrt{2} :! : 2$

$\sqrt{2} : 1 : 2$

$2 : 1 : \sqrt{2}$

answer is B.

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Detailed Solution

Let the initial pressure of the three samples be $P_{A}, P_{B} a n d P_{C}$ , then

$P_{A} {(V)}^{\frac{3}{2}} = {(2 V)}^{\frac{3}{2}} P, P_{B} = P$

$a n d P_{C} v = P (2 v)$

$P_{A} : P_{B} : P_{C} = {(2)}^{\frac{3}{2}} : 1 : 2$

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