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Ideal Gas Equation

Two closed bu...

Question

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $p_{1}$ 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:

2 p_{f} (\frac{T_{1}}{T_{1} + T_{2}})

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2 p_{f} (\frac{T_{2}}{T_{1} + T_{2}})

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2 p_{f} (\frac{T_{1} T_{2}}{T_{1} + T_{2}})

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2 p_{f} (\frac{T_{1} T_{2}}{T_{1} + T_{2}})

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Solution

The correct option is B $2 p_{f} (\frac{T_{2}}{T_{1} + T_{2}})$
Initial moles = final moles
$\frac{P_{i} \times V}{R T_{1}} + \frac{P_{i} \times V}{R T_{1}} = \frac{P_{f} \times V}{R T_{2}} + \frac{P_{f} \times V}{R T_{1}}$
$\frac{P_{i}}{T_{1}} + \frac{P_{i}}{T_{1}} = \frac{P_{f}}{T_{2}} + \frac{P_{f}}{T_{1}}$
$\frac{2 P_{i}}{T_{1}} = P_{f} [\frac{1}{T_{2}} + \frac{1}{T_{1}}]$
$\frac{2 P_{i}}{T_{1}} = P_{f} [\frac{T_{1} + T_{2}}{T_{1} T_{2}}]$

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