# Definition of heat and temperature

Does your cup of coffee contain heat? Does it contain temperature? Explain.

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#### Solution Preview

Heat and temperature are not fundamental properties of physical objects. These quantities only have a meaning at the level of a statistical description of physical objects. It is analogous to considering the average weight of people in a group and then asking if the group contains this average. While you can calculate it from the properties of the system, it only exists at the group level as a statistical quantity.

To be able to describe the macroscopic world we can observe in a tractable way, requires one to be able to eliminate the detailed physics of microscopic world of atoms and molecules that the macroscopic objects consists of. While we may also be interested in atoms and molecules, physics would not be useful in practice if you could not describe the behavior of things like a cup of coffee without having to invoke all the details of 10^25 molecules. The problem we then face is that the laws of physics don't allow for decoupling of the macroscopic and microscopic degrees of freedom of a system.

Take e.g. a ball that can collide with other balls. We know that we can describe the physics here using conservation of momentum and conservation of energy. Suppose that we take into account that the ball is not a point mass and that it consists of a large number of molecules. Then as far as conservation of momentum is concerned, there is no problem, because the sum of the momenta of all the molecules equals the momentum of the center of mass of the ball. But the total energy of the molecules is not equal ...

#### Solution Summary

We explain in detail how heat and temperature are defined.