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Question

A gas expands from volume $V_{1}$ to volume $V_{2}$ according to three different processes 1, 2 and 3. Change in internal energy of the gas in the processes are $Δ U_{1}, Δ U_{2}$ and $Δ U_{3}$ respectively. If same quantity of heat is supplied in three cases, then

Moderate

A

$Δ U_{1} < Δ U_{2} < Δ U_{3}$
B

$Δ U_{1} > Δ U_{2} > Δ U_{3}$
C

$Δ U_{2} < Δ U_{3} > Δ U_{1}$
D

$Δ U_{1} > Δ U_{3} < Δ U_{2}$

Solution

By first law of thermodynamics, $Δ Q = Δ U + Δ W \Rightarrow Δ U = ∆ Q - Δ W$
Now $Δ W_{1} > Δ W_{2} > Δ W_{3}$
$∴ Δ U_{1} < Δ U_{2} < Δ U_{3}$

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