Why isn’t it sufficient to describe temperature as heat density?

Question

Why isn’t it sufficient to describe temperature as heat density?

In: Physics

Answer 1

The simple answer is that you have

stored heat = temperature * heat capacity

a load of water can contain a lot of “heat” at a low temperature, so that it’s really good for pulling heat out of hot objects, because the heat will keep flowing into the water until the *temperatures* balance, not the *amounts of heat ,* with the water ending up with much more of the heat to reach the same temperature.

It gets more complicated, usually we split heat capacity into

mass * specific heat capacity

So that we can talk about the heat given to a large or small amount of water. Then you could use the actual density of water and say:

stored heat/volume = temperature * specific heat capacity * mass/volume

or

heat density = temperature * specific heat capacity * mass density

So there is a connection between temperature and heat density in these situations, but it’s not them being the same thing.

But then things get even more complicated when you start to think about objects for which the relationship is not simple multiplication, because at different temperatures the specific heat capacity changes.

But that’s the basic thing.