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Displacement in 1-D

A given mass ...

Question

A given mass of gas expands from the state $A$ to the state $B$ by three paths 1, 2 and 3 as shown in the figure. If $W_{1}, W_{2}$ and $W_{3}$ respectively be the work done by the gas along three paths then:

W_{1} > W_{2} > W_{3}

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W_{1} < W_{2} < W_{3}

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W_{1} = W_{2} = W_{3}

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W_{1} < W_{2}; W_{1} < W_{3}

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Solution

The correct option is C $W_{1} < W_{2} < W_{3}$
Work done can be calculated by calculating the area under $P - V$ diagram.

Let $A_{1}$ , $A_{2}$ and $A_{3}$ be the area under the $P - V$ graph for $1$ , $2$ and $3$ process respectively.

$A_{1} < A_{2} < A_{3}$

$∴ W_{1} < W_{2} < W_{3}$

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