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A container is separated into two 1 litre compartments by a piston of negligible mass as hown below. In lower compartment 0.1 mole of an ideal monoatomic gas is filled at 0.1 bar pressure and the other compartment is empty. Now the stoppers are removed so that the gas expands to 2 litre. Heat is supplied to the gas so that finally pressure of gas equals to 0.1 bar. Calculate $Δ H$ of the process in joule. [1 bar litre = 100 J]

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answer is 25.

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Detailed Solution

We know that,

$P_{1} V_{1} = P_{2} V_{2}$

$0.1 \times 1 = P_{2} \times 2$

$\begin{array}{l} P_{2} = \frac{0.1}{2} \\ T_{1} = \frac{0.1 \times 1}{0.083 \times 0.1} \\ \frac{P_{2}}{T_{1}} = \frac{P_{3}}{T_{2}} \end{array}$

$\Rightarrow T_{2} = (\frac{0.1 \times 2}{0.1}) \times \frac{1}{0.083}$

$Δ H = 0.1 \times \frac{5}{2} \times 8.3 \times \frac{1}{0.083} = 25 J$

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