Question
Deduce first law of thermodynamics for $: (a)$ isothermal process $(b)$ isochoric process

Answer

First law of thermodynamics: $\Delta U=Q+W$
$(a)$ For isothermal process, $\Delta U=0$.
$\therefore \ 0=Q+W$
$\therefore \ Q=-W$
$(b)$ For isochoric process, $\Delta V=0$.
$\therefore \ \Delta U=Q+W$
$\therefore \ \Delta U=Q+\left(-P_{\text {ext }} \cdot \Delta V\right) \ldots \ldots (W = -P_{ext}.\Delta V)$
$\therefore \ \Delta U=Q+0$
$\therefore \Delta U=Q_v$

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