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Heat Capacity

A gas undergo...

Question

A gas undergoes A to B through three different processes 1, 2 and 3 as shown in the figure. The heat supplied
to the gas is $Q_{1}, Q_{2}$ and $Q_{3}$ respectively, then

A

Q_{1} = Q_{2} = Q_{3}

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B

Q_{1} < Q_{2} < Q_{3}

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C

Q_{1} > Q_{2} > Q_{3}

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D

Q_{1} = Q_{3} > Q_{2}

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Solution

The correct option is C $Q_{1} > Q_{2} > Q_{3}$

We know that in P-V graph, the work done for clockwise path is positive and negative for anticlockwise path. So,
$Δ W_{1} = (+) v e, Δ W_{2} = 0, Δ W_{3} = (-) v e$

Internal energy depends on the initial and final points and is path independent. So,
$Δ U_{1} = Δ U_{2} = Δ U_{3}$

We know that, $Δ Q = Δ U + Δ W$ and $Δ U$ is same for all the three processes,
$S o, Q_{1} > Q_{2} > Q_{3}$

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