= Refrigerator
A refrigerator removes <heat> from the region we want to keep cold and releases <heat> to warmer surroundings. Here we consider a work-driven cyclic device: its useful output is the cold-side extraction $Q_c$, and its input is net <work> $W$. A food compartment is a familiar example; the same cooling objective applies when removing <heat> from a room. The <coefficient of performance> measures extraction per unit <work>, rather than the fraction of input <energy> converted into output. https://openstax.org/books/university-physics-volume-2/pages/4-3-refrigerators-and-heat-pumps[Ling, Moebs and Sanny, University Physics Volume 2, §4.3: refrigerators and useful output]{ref}
Choose the complete machine as the <thermodynamic system>. Let $Q_c>0$ be <heat> entering from the colder side, $Q_h>0$ be <heat> delivered to the hotter side, and $W>0$ be net <work> supplied, all over the same complete cycle. Assume these are its only <energy> transfers, no matter crosses the outer boundary, and there is no net change in stored <energy>. Returning to the initial state gives $\Delta U=0$, so the <first law of thermodynamics> reads
$$
0=Q_c-Q_h+W,\qquad Q_h=Q_c+W.
$$
The <heat> leaving the warmer side includes both the extracted <heat> and the supplied <work>. For instance, stipulated transfers $Q_c=3\,\mathrm{kJ}$ and $W=1\,\mathrm{kJ}$ require $Q_h=4\,\mathrm{kJ}$; the cooling <coefficient of performance> is $3$. This is an illustrative budget, not measured performance. At steady operation the same balance holds for average transfer rates, $\dot Q_h=\dot Q_c+P_{\rm in}$, where $P_{\rm in}$ is input <power>.
This budget explains a useful counterexample: operating a <refrigerator> with its door open inside an otherwise isolated room cannot cool the room as a whole. If both <heat> transfers occur within the room and the electrical input comes from outside, the room gains $Q_h-Q_c=W$ each cycle. Locally cold air does not imply net cooling. The <Second law of thermodynamics> permits cold-to-hot transfer because <work> is supplied; it forbids a cyclic device whose sole effect is that transfer. See the <Clausius statement of the second law>.
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