• Pixel-art sticker of Pumpa, personifying Heat Pump, with the caption “Move Heat, Don't Make It.”

IndexHeat & EntropySticker

Pumpa

Heat Pump Physics

\[\text{COP}_{\max} = \frac{T_h}{T_h - T_c}\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Pumpa, a heat pump who moves heat and doesn't make it: she uses work to move heat from cold to hot. Heating at 20 °C from 0 °C outside, her ideal maximum COP is about 14.7. Real heat pumps reach less than this. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Pumpa, a heat pump who uses a little work to move a lot of heat from cold to hot.

Heat flows naturally from hot to cold. A heat pump runs it the other way. It uses work, usually from an electric compressor, to pull heat from cold outdoor air and deliver it indoors. Its performance is measured by the coefficient of performance (COP): heat delivered divided by work put in. The second law of thermodynamics sets the ideal maximum, the Carnot limit, at T_h/(T_h − T_c), with temperatures in kelvin.

Example: heating a house at 20 °C (293.15 K) from 0 °C outside gives an ideal maximum COP of about 293.15/20 ≈ 14.7 (computed). In other words, a perfect heat pump would deliver almost fifteen joules of heat for every joule of work.

Real heat pumps reach much less, typically COPs of 2 to 5 in practice, because of friction, finite temperature differences in the heat exchangers and other losses. Even so, they deliver several times more heat than the electricity they use, which is why they are efficient for heating homes. Refrigerators run the same cycle to move heat out.

The colder it is outside, the lower the COP.

Equations

\[\text{COP}_{\max} = \frac{T_h}{T_h - T_c}\]
Symbols
SymbolMeaningUnit
\(\text{COP}_{\max}\) ideal maximum coefficient of performance for heating —
\(T_h\) absolute temperature of the warm side \(\mathrm{K}\)
\(T_c\) absolute temperature of the cold side \(\mathrm{K}\)