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Difference between Internal Energy and Enthalpy

A gas is expa...

Question

A gas is expanded from volume $V_{0}$ to $2 V_{0}$ under three different processes. Process $1$ is isobaric process, process $2$ is isothermal and process $3$ is adiabasic. Let $△ U_{1}, △ U_{2}$ and $△ U_{3}$ be the change in internal energy of the gas in these three processes. Then

△ U_{1} > △ U_{2} > △ U_{3}

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△ U_{1} < △ U_{2} < △ U_{3}

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△ U_{2} < △ U_{1} < △ U_{3}

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△ U_{2} < △ U_{3} < △ U_{1}

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Solution

The correct option is A $△ U_{1} > △ U_{2} > △ U_{3}$
For process $(1) :$ Isobaric
$\Rightarrow △ W = P △ V$
$\Rightarrow P V = n R T$
$\Rightarrow P △ V = n R △ T$
$\Rightarrow △ T = \frac{△ W}{n R}$
$\Rightarrow △ U = \frac{n R}{(r - 1)}, △ T = \frac{n R}{r - 1} . \frac{△ W}{n R}$
$\Rightarrow U_{1} = \frac{△ W}{r - 1}$
For process $(2) :$ Isothermal $: △ T = 0$
$\Rightarrow U_{2} = 0$
For process $(3) :$ Adiabatic $: △ Q = 0$
$\Rightarrow △ W = - △ u$
$\Rightarrow U_{3} = - △ W$
$\Rightarrow \frac{n R}{(r - 1)} △ T = △ W$
$\Rightarrow △ T = \frac{△ W (r - 1)}{n R}$
So, $U_{1} > U_{2} > U_{3}$

Hence, the answer is $U_{1} > U_{2} > U_{3} .$

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A gas is expanded from volume V0 to 2V0 under three different processes. Process 1 is isobaric process, process 2 is isothermal and process 3 is adiabasic. Let △U1,△U2 and △U3 be the change in internal energy of the gas in these three processes. Then

A gas is expanded from volume $V_{0}$ to $2 V_{0}$ under three different processes. Process $1$ is isobaric process, process $2$ is isothermal and process $3$ is adiabasic. Let $△ U_{1}, △ U_{2}$ and $△ U_{3}$ be the change in internal energy of the gas in these three processes. Then