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Dalton's Law of Partial Pressures

Two closed bu...

Question

Two closed bulbs of equal volume (v) containing an ideal gas initially at pressure $P_{4}$ 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 $T_{2}$ . What is the final pressure $P_{f}$ ?

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Solution

Let us consider the problem:

$n_{1} + n_{2} = n_{1}^{'} + n_{2}^{'}$

Therefore,
$\frac{p_{i} V}{R T_{1}} + \frac{p_{i} V}{R T_{1}} = \frac{p_{f} V}{R T_{1}} + \frac{p_{f} V}{R T_{2}}$

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

=> $P_{f} = \frac{2 p_{i} T_{2}}{T_{1} + T_{2}}$

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