Select the correct observation for a 8.21 litre container, filled with 2 moles of He at 300K)

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It has pressure 6 atm.

If it is closed non-rigid (like thin skin balloon), its volume increases to 16.42 lit on heating to 600K.

If it is an open rigid container, its pressure increases to 8 atm on heating to 400K.

When connected with another similar empty container maintained at 150K while maintaining original container at 300K, pressure reduced to $\frac{2}{3} atm$

answer is A, C.

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Detailed Solution

Given,

Volume $= 8.21 L$

$\begin{array}{l} n_{re} = 2 moles \\ T = 300 K \end{array}$

From ideal gas equation,

$\begin{array}{l} p v = n R T \\ P \times 8.21 = 2 \times 0.0821 \times 300 \\ P = 6 atm \end{array}$

Open container

$P = Pgas + Patm .$

$Pages = \frac{2 \times 0.821 \times 400}{8.21} = 8 atm$

so, pressure will be more than 8 atm
closed non rigid (P= constant)

$\begin{array}{l} \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}, \frac{8.21}{300} = \frac{V_{2}}{600} \\ v_{2} = 16.42 \\ \frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}, \frac{6}{300} = \frac{P_{2}}{150} \\ P_{2} = 3 atm, P_{1} = 6 a + m \end{array}$