Average kinetic energy/ temperature confusion

[Bengo]

My mcat book says temperature is a measure of the total kinetic energy of a system. Then later on it says temperature is a measurement of the average kinetic energy of a system. Is this an error? Thank you.

 

[PhysicoRaj]

The second statement is correct. The first one refers to heat content.

 

[Bengo]

Are average kinetic energy and temperature the same thing?

 

[Yanick]

In a given system of particles at a given temperature their is a distribution of kinetic energies, some are slower and some are faster. Classical mechanics, and some statistics, can be used to relate the average kinetic energy of the system to the temperature of the system. You can read some more about this if you check out the Kinetic Theory of Gases. Without more details regarding the statement we cannot rule either statement out as incorrect because the higher the average kinetic energy the higher the total kinetic energy which are in fact proportional to the temperature. Don't forget that averages are sums divided by the population of the sample. So total kinetic energy is the sum of the kinetic energies of the particles and the average KE differs from the total by a constant (the number of bodies). In the context of the gross oversimplification related to physical science training of healthcare providers we can say that each statement is correct.

 

[adjacent]

A simple example to help you understand the difference between the average and the total kinetic energy:
You have an electric kettle and a swimming pool both at 100°C.
Obviously the swimming pool will have more heat energy(total kinetic energy) because it has more number of particles/atoms.

However,they both have the same temperature.

It's because the energy per particle stays constant(Total kinetic energy/Total number of particles)
As the number of particles increase in the swimming pool,the heat energy also increases proportionally,if the temperature is constant.