= Heat pump
A heat pump uses <work> to deliver <heat> to the region we want to keep warm. Its useful output is the hot-side delivery $Q_h$. The same operating machine can be described as a <refrigerator> when the cold-side extraction $Q_c$ is the objective: which output is useful changes the <coefficient of performance>, while the <energy> balance stays $Q_h=Q_c+W$. Heating a water bath by taking <heat> from a colder water bath makes this distinction visible in the <heat-pump calorimetry> experiment below. https://labs.phys.utk.edu/mbreinig/phys136core/modules/m3/refrigerators.html[University of Tennessee, Refrigerators, air conditioners, and heat pumps: heating objective]{ref}
In the illustrative budget from <refrigerator>, supplying $1\,\mathrm{kJ}$ of <work> delivers $4\,\mathrm{kJ}$ of useful <heat>, giving a heating <coefficient of performance> of $4$. The additional $3\,\mathrm{kJ}$ came from the colder region. Compare an ideal electrical heater whose entire input <work> becomes <heat> in the target region: it delivers $1\,\mathrm{kJ}$ for that input. The appeal of a <heat pump> is this ability to move existing <energy>, while the <Second law of thermodynamics> limits the <work> saving for a given pair of <temperatures>.
\Image[/heat-pump-energy-and-carnot-bounds.png]
{title=One <energy> budget, two useful outputs, and <Carnot's theorem> bounds on the <coefficient of performance>}
{description=Original quantitative diagram, with stipulated $Q_c=3\,\mathrm{kJ}$, $W=1\,\mathrm{kJ}$ and $Q_h=4\,\mathrm{kJ}$. Arrow widths follow the $3:1:4$ transfer magnitudes. The curves are reversible bounds for fixed cold <temperature> $T_c=280\,\mathrm K$ and varying hot <temperature> $T_h=T_c+\Delta T$; they are not measured performance. At $\Delta T=40\,\mathrm K$, the bounds are $7$ for cooling and $8$ for heating, above the illustrative machine's $3$ and $4$.}
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