# Specific heat/capacity, which cools faster?

syntotic
Which material will cool faster, one with a higher specific heat/capacity index or one with a lower value?

## Answers and Replies

Staff Emeritus
Science Advisor
Homework Helper
Cooling rate depends on temperature difference with an object's surroundings, among other things. All the specific heat capacity will tell you is how much heat per unit mass the material can absorb for a temperature change of 1 degree.

syntotic
mmm... Bismuth would cool faster than water then, because it absorbs less heat to change temperature one degree?

Science Advisor
Possibly, but there's no guarantee of that. Other factors are involved, especially in your example where one substance is a liquid and one is solid.

Gold Member
Well, the 1D heat conduction equation is
$\frac{dT}{dt}=\frac{k}{\rho Cp}\frac{d^2T}{dx^2}$
so a larger Cp would result in a smaller thermal diffusivity, and therefore an object with large Cp would respond slower to temperature changes (because of what SteamKing said).

syntotic
Ecco.

Mentor
The word cooling is poorly defined here. It can mean the rate of heat loss or temperature change. So heat transfer coefficient can matter too.

Science Advisor
Homework Helper
Gold Member
If you assume everything is identical except the SHC and that "cools faster" means the temperature falls faster then the one with the lower SHC will cool faster.

If they both start at the same temperature the one with the higher SHC will start with more energy. If the heat loss in joules/second is the same for both the one with the highest SHC will stay hot for longer.