Temperature and Kinetic Energy

[tomtraxler]

If temperature is defined as the average kinetic energy of molecules in a fluid (or gas), then why isn't the temperature of a fluid increased when that fluid is set in motion? Or is it?

For example, if a stationary fluid is set into motion, do the molecules not have additional kinetic energy, like taking a cup of water and moving it or by making it swirl with a spoon? The energy relative to each other molecule might be the same, but relative to some external standard, it has increased.

 

[Clausius2]

Very good question. It is the kind of question I ask to my pillow every night. You are mixing the relativity of reference frames with thermodynamics.

I'm not going to answer you quantitatively but qualitatively. In classical thermodynamics, the velocity is referred to an inertial frame that is attached with the center of mass of the gas. Any other external velocity, such a traslative velocity you mentioned does not increase the internal energy, but the kinetic energy of the whole system. The static Temperature, as we call to that Temperature obtained by the average kinetic energy of the molecules. That is the real temperature of the gas, because despites it is moving globally with some velocity, if you want to measure experimentally the Temperature you will obtain the average of the molecular kinetic energy, without the velocity of your external reference frame.

On the other hand, the apparent Temperature of the system is what we call the Total Temperature. In fact, if the acceleration process of the reservoir is made isentropically:

$$c_pT_o=c_pT+\frac{1}{2}*v^2$$ is yielded by the energy conservation:

$$T_o=T+\frac{v^2}{2c_p}$$

where To=Total Temperature (external, apparent, depending on the reference frame);
T=Static Temperature (internal, the experimental temperature, it is obtained from the equation of State).
v=velocity of the whole mass of gas.

When you put a thermometer inside the reservoir, you are measuring the Static Temperature (v=0).

 

[Tide]

If temperature is defined as the average kinetic energy of molecules in a fluid (or gas), then why isn't the temperature of a fluid increased when that fluid is set in motion? Or is it?

For example, if a stationary fluid is set into motion, do the molecules not have additional kinetic energy, like taking a cup of water and moving it or by making it swirl with a spoon? The energy relative to each other molecule might be the same, but relative to some external standard, it has increased.

Temperature is a measure of the squared deviation of velocity about the mean. Simply moving an object has no effect on the mean squared deviation.

 

[tomtraxler]

Excellent responses. Thanks for explaining it to me.