ExplainerTools · Thermodynamics · Original

Heat Pump: Moving Heat Uphill

How can electricity move more heat than it makes?

Why it changes

A 45 K climb: every 1 kW of electricity delivers 3.54 kW of heat.

Pins 55 °C delivery, then drops it to 35 °C at the same 1 kW.

Change the climb

0 °C

Colder air starts the climb lower.

45 °C

Hotter radiators or air raise the top of the climb.

1.00 kW

Scales every flow; sets the animation pace.

Energy ledger · each second

Illustrative model
Heat from outdoor air2.54kW
Electrical work1.00kW
Heat delivered indoors3.54kW

Amber block = 1× the electricity. Dotted line = Carnot ceiling (7.07×); the model reaches 50% of it.

Why lift matters

COP ≈ ½ × Tdelivery(K) ÷ lift. Bright segment: lifts reachable at this delivery temperature.

How the four stages move heat uphill

    Heat flows only from hot to cold on its own. The trick is to make the refrigerant colder than the outdoor air for stage 1 and hotter than the delivery temperature for stage 3. The compressor's work pays for that climb, and a bigger climb costs more work per unit of heat.

    Model, units and assumptions

    PhysicsEnergy balance (delivered = extracted + work) and the Carnot limit for a heat pump, COPCarnot = Thot ÷ (Thot − Tcold), with temperatures converted to kelvin (+273.15) before dividing.

    IllustrativeCOP = 0.5 × COPCarnot. The 50% figure is a teaching assumption, not a measured value. Delivery and outdoor temperatures stand in for the refrigerant's real hot and cold temperatures. All kW figures and scene band widths are model outputs. Band widths are drawn to scale relative to 1× the electrical input, so the input slider changes the kW numbers and flow pace while the proportions stay put.

    Not shownNo measured appliance data. Out of scope: equipment capacity limits, defrost, on/off cycling, heat-exchanger approach temperatures, specific refrigerants and their properties, fan and pump power. Real units at small lifts fall well short of the high COPs this ceiling allows; the trend with lift, not the exact numbers, is the lesson.

    Sources