First slide

Work done by gas

Question

An ideal gas goes from state A to state B via three different processes A as indicated in the p -V I diagram lf $Q_{1}, Q_{2}, Q_{3}$ indicate the heat absorbed P by the gas along the three processes and $∆ U_{1}, ∆ U_{2}, ∆ U_{3}$ indicate the change in internal energy along the three processes respectively, then

Moderate

A

$Q_{1} > Q_{2} > Q_{3} and ∆ U_{1} = ∆ U_{2} = ∆ U_{3}$
B

$Q_{1} > Q_{2} > Q_{1} and ∆ U_{1} = ∆ U_{2} = ∆ U_{3}$
C

$Q_{1} = Q_{2} = Q_{3} and ∆ U_{1} > ∆ U_{2} > ∆ U_{3}$
D

$Q_{1} > Q_{2} > Q_{3} and ∆ U_{1} > ∆ U_{2} > ∆ U_{3}$

Solution

For all processes 1,2 arrd3
$∆ U = U_{B} - U_{A}$ is the same
$∴ ∆ U_{1} = ∆ U_{2} = ∆ U_{3}$
Now, $Q$ = $∆ U$ + W
Now, W = work done by the gas
$∴ Q_{1} > Q_{2} > Q_{3}$

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