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Two closed containers of equal volume of air are initially at $1.05 \times 10^{5} P a$ pressure and 300K temperature. IF the containers are connected by a narrow tube and one container is maintained at 300K temperature and other at 400K temperature. The final pressure (in kPa) in the containers is _____________

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answer is 120.

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Detailed Solution

$\frac{P_{0} V_{0}}{T_{0}} + \frac{P_{0} V_{0}}{T_{0}} = P V_{0} (\frac{1}{300} + \frac{1}{400})$

$2 \frac{P_{0} V_{0}}{T_{0}} = P V_{0} (\frac{1}{300} + \frac{1}{400}) \Rightarrow p = \frac{2 P_{0}}{T_{0}} (\frac{300 \times 400}{700})$

$p = \frac{2 \times 1.01 \times 10^{5}}{300} \times \frac{300 \times 400}{700} = 120 k P_{a}$

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