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System, Surroundings, Intensive, Extensive Properties

Two closed bu...

Question

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $p_{i}$ and temperature $T_{1}$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_{2}$ .The final pressure $p_{f}$ is:

A

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B

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C

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D

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Solution

The correct option is B

No. of moles initially = no. of moles finally

$\Rightarrow \frac{p_{i} V}{R T_{1}} + \frac{p_{i} V}{R T_{1}} = \frac{p_{f} V}{R T_{1}} + \frac{p_{f} V}{R T_{2}} \Rightarrow \frac{2 p_{i}}{T_{1}} = p_{f} (\frac{1}{T_{1}} + \frac{1}{T_{2}}) \Rightarrow \frac{2 p_{i}}{T_{1}} (\frac{T_{1} T_{2}}{T_{1} T_{2}}) = p_{f} \Rightarrow p_{f} = 2 p_{i} (\frac{T_{2}}{T_{1} + T_{2}})$

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