First slide

Change in internal energy

Question

100 mol of an ideal gas is heated from 10° to 20°C keeping its (i) volume constant (ii) pressure constant.
Let $Δ U_{a}$ and $Δ U_{b}$ denote the change in the internal energy of the gas due to process (i) and (ii),
respectively. Then, which of the following shall be true?

Moderate

A

$Δ U_{a}$ = $Δ U_{b}$
B

$Δ U_{a}$ > $Δ U_{b}$
C

$Δ U_{a}$ < $Δ U_{b}$
D

$Δ U_{a}$ = $Δ U_{b}$ = 0

Solution

(i) Volume is constant,
$i.e. Δ V = 0$
$\Rightarrow Δ U_{a} = Q - p Δ V$
$\Rightarrow Δ U_{a} = Q$
(ii) Pressure is constant,
$i.e. Δ p = 0$
$\Rightarrow Δ U_{b} = Q - p Δ V$
$∴ Δ U_{a} > Δ U_{b}$

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