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Two different...

Question

Two different adiabatic paths for the same gas intersect two isothermal $T_{1} a n d T_{2}$ as shown in the P-V diagram. Then $V_{a} / V_{d}$ is equal to

A

\frac{V_{c}}{V_{b}}

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B

V_{C} V_{b}

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C

\frac{V_{b}}{V_{c}}

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D

\frac{V_{C} V_{b}}{V_{c} + V_{b}}

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Solution

The correct option is C $\frac{V_{b}}{V_{c}}$
$T_{1} (V_{a})^{v - 1} = T_{2} (V_{d})^{v - 1} \frac{T_{1}}{T_{2}} = {[\frac{V_{d}}{V_{a}}]}^{v - 1}$
Also
$T_{1} (V_{b})^{v - 1} = T_{2} (V_{c})^{v - 1} \frac{T_{1}}{T_{2}} = {[\frac{V_{c}}{V_{b}}]}^{v - 1} \frac{V_{a}}{V_{d}} = \frac{V_{b}}{V_{c}}$

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