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Standard XII

Chemistry

PV Work

One mole of a...

Question

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph above. If the work done along the solid line path is $w_{s}$ and that along the dotted line path is $w_{d}$ , then the integer closest to the ratio $w_{d} / w_{s}$ is :

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Solution

The correct option is B 2
For calculating work done, we need to calculate the area under curve for solid and dotted lines.
Let $^{'} w_{d}^{'}$ and $^{'} w_{s}$ be work done along the dotted and solid path respectively.
$w_{d} = 4 \times 1.5 + 1 \times 1 + 2.5 \times 2 / 3 = 8.65$
Process is isothermal.
$w_{s} = 2 \times 2.303 log \frac{5.5}{0.5} = 2 \times 2.303 \times l o g 11 = 2 \times 2.303 \times 1.0414 = 4.79$
$\frac{w_{d}}{w_{s}} = \frac{8.65}{4.79} = 1.80 ≃ 2$

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