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Q.

Two closed vessels of equal volume containing air at pressure $P_{1}$ and temperature $T_{1}$ are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at $T_{1}$ and that in the other at $T_{2},$ what will be the pressure in the vessels ?

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a

$\frac{2 P_{1} T_{2}}{T_{1} + T_{2}}$

b

$\frac{2 P_{1}}{T_{1} + T_{2}}$

c

$\frac{T_{1}}{2 P_{1} T_{2}}$

d

$\frac{2 P_{1} T_{1}}{T_{1} + T_{2}}$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{P_{1}}{T_{1}} + \frac{P_{1}}{T_{1}} = \frac{P}{T_{1}} + \frac{P}{T_{2}} \\ \frac{2 P_{1}}{T_{1}} = P (\frac{T_{1} + T_{2}}{T_{1} T_{2}}) \\ ∴ P = \frac{2 P_{1} (T_{1} T_{2})}{T_{1} (T_{1} + T_{2})} = \frac{2 P_{1} T_{2}}{T_{1} + T_{2}} \end{array}$

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