# Temperature as a measure of thermal energy

1. Apr 29, 2015

### Mr Davis 97

I am little confused as to why temperature is a measure of thermal energy. Thermal energy is defined as the total internal kinetic energy of an object. Temperature, on the other hand, is defined as the measure of the average kinetic energy of an object, or the thermal energy per particle. If temperature only measures the average kinetic energy of each particle, then how does this measure thermal energy of an object, when there are other factors involved such as the size of the object. Say we have two containers of the same size. Container 1 has one particle moving at X m/s. Now imagine a second container. It as 10 particles moving at X m/s. Both of these containers have the same average internal kinetic energy, but container two has more internal kinetic energy. Could someone please explain why we use to temperature to measure thermal energy?

2. Apr 29, 2015

### rumborak

As you point out yourself, it's about the thermal energy per particle. If you have 10 particles instead of one, your denominator is also 10. If you have only one particle, you divide by just one. Either way, the energy per particle will be the same.
This is assuming you are disregarding the boxes themselves in that calculation. If you want to include them, you should for simplicity assume they are the same temperature as the particles they contain. In which case all you're doing is adding more particles to the denominator.
If the boxes are not the same temperature as the particles inside, well, the you'd be comparing apples with oranges, since the average temperature of the two boxes will differ.

3. Apr 29, 2015

### nasu

We don't. Two objects with the same temperature can have vastly different thermal energies. Compare the thermal energies of a drop of water and the ocean, both at 20 degrees. Which one has more thermal energy?