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A vessel contains 8 gm of air at 500K. Some amount of air leaks out through the hole provided to it. After some time, the pressure is halved and the temperature is changed to 400 K. Find the mass of the air escaped in gm.

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answer is 3.

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Detailed Solution

m₁ = 8gm, m₂ = m₁ - $∆$ m
From ideal gas equation
$\begin{array}{l} Pv = nRT = \frac{m}{M} RT \\ P_{1} = m_{1} T_{1} \\ P_{2} = m_{2} T_{2} \\ \frac{P_{1}}{P_{2}} = (\frac{m}{m_{1} - Δm}) \frac{T_{1}}{T_{2}} \\ ∆ m = 3 g \end{array}$

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