Three samples of the same gas A, B and C( = 3/2) have initially e… - Vidyadip

Question

Three samples of the same gas $A, B$ and $C(\gamma = 3/2)$ 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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Answer

(b) Let the initial pressure of the three samples be ${P_A},\,{P_B}$ and ${P_C}$, then ${P_A}{(V)^{3/2}} = {(2V)^{3/2}}P$, ${P_B} = P$ and

${P_C}(V) = P(2V)$

==> ${P_A}\,:\,{P_B}\,:\,{P_C} = {(2)^{3/2}}:\,1\,\,:\,\,2 = 2\sqrt 2 \,:\,1\,:\,\,2$

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