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Heat Capacity

If w1, w2...

Question

If $w_{1}$ , $w_{2}$ , $w_{3}$ and $w_{4}$ are work done in isothermal, diabatic, isobaric and isochoric reversible processes, respectively then the correct sequence (for expansion) would be:

A

w_{1} < w_{2} < w_{3} < w_{4}

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B

w_{3} = w_{2} = w_{1} = w_{4}

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C

w_{3} < w_{2} < w_{4} < w_{1}

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D

w_{3} > w_{1} > w_{2} > w_{4}

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Solution

The correct option is D $w_{3} > w_{1} > w_{2} > w_{4}$
Since $W = \int P d V$

where $\int P d V$ is simply the area enclosed by the $P - V$ curve under volume axis. For the given curve, it may be observed that the area enclosed by the isobaric process is maximum followed by the isothermal, adiabatic and Isochoric process.

Since for the same amount of expansion,
$A r e a_{I s o b a r i c} > A r e a_{I s o t h e r m a l} > A r e a_{A d i a b a t i c} > A r e a_{I s o c h o r i c}$

Therefore the work done will also follow the same order,i.e,
$w_{3} > w_{1} > w_{2} > w_{4}$

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