Would heating a space up to 50c require the same amount of energy as cooling it down to -50?

Question

Lets assume we have a 0.5 square meter box, sitting in an envoirement that is 0c.

Would it take the same amount of energy to heat the box up to 50c as it would take to cool that box down to -50c?

Assuming the exact same box is in the exact same location with the exact same surroundings

In: 6

Answer 1

No, and I’ll explain from a different standpoint than the other current answers.

0°C is a highly relevant temperature to us humans, being the freezing point of water, but it’s not particularly special from a physics perspective. The Kelvin scale is used to measure temperature from an absolute standpoint, and is much more applicable to this kind of question. 0°C is 273.15°K.

[Thermal Conductivity] is a property of matter that indicates its ability to transfer heat energy within its internal structure. Higher thermal conductivity allows for faster heat transfer from a heat source to a heat sink, whereas lower thermal conductivity causes the opposite. Notably, Thermal Conductivity of materials varies (usually non-linearly) with the current temperature of the material.

[Thermal Conductivity]: https://en.wikipedia.org/wiki/Thermal_conductivity

Thermal Conductivity is usually expressed as a function of the temperature of the material in Kelvin, as the absolute scale makes the math much simpler.

All of this is background to say the following:

For every unit of heat you pump into a material, the next unit of heat costs an additional amount of energy to pump in. For every unit of heat you pump _out_ of a material, the next unit costs _less_ energy to pump out.

This is all before you get into the efficiency of the actual heat pump mechanism itself, which has its own issues. Pumping heat into a material inherently costs less energy overall as you only have to supply the heat itself and a small amount of overage to cover the material of the heating element, whereas pumping heat out of a material requires you to perform the same transfer of energy, but then dump it somewhere that is isolated from the target material, which an additional energy expenditure, and a waste of the dumped heat energy.

As to which is more efficient, it depends upon specifics, but it’s definitely not a 1:1.