# Does temperature depend on velocity of observer [duplicate]

This question already has an answer here:

The kinetic theory of gases states that temperature is a function of the average kinetic energy of a gas particle. But for the sake of our experiment lets say we have system of 5 molecules each of which are travelling in the same line (positive x direction) with different velocities (5$\frac{m}{s}$,10$\frac{m}{s}$,13$\frac{m}{s}$,43$\frac{m}{s}$,24$\frac{m}{s}$). So to an observer moving in the same direction as the molecules with the velocity (10$\frac{m}{s}$) the molecules in question appear to slowly and hence their velocity is reduced (from the perspective of moving observer). So according to:

1. Moving observer: Particles are moving slowly so their kinetic energy and hence temperature (correct me if I am wrong) so these gases would be colder
2. Ground based observer: Particles are moving fast therefore the temperature of the system is high

## marked as duplicate by John Rennie, Ruslan, sammy gerbil, Yashas, Community♦Mar 10 '17 at 16:51

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• – John Rennie Mar 10 '17 at 15:59

## 2 Answers

Temperature defined theoretically is a beautifull concept, however is interesting to answer the question regarding how the temperature is measured.

Consider a cloud of gas or any other object. As a first approximation, suppose that the cloud behaves as a blackbody. As a black body, the cloud will emit radiation in and it is that what we can observe and measure, therefor its temperature can be measured indirectly observing the spectrum thanks to the Wien's law.

Consider now the same system but the observer is moving relative to the cloud. The spectrum will be squized or streched depending on the velocity. Hence, the temperature is relative to the observer.

Temperature is based on the average K.E. distribution of a system. K.E. is based on a velocity (v) component. When you answer this question, focus on the relative velocities of the system; particles moving in a straight line have K.E. relative to the frame of interaction (the velocity is only relative to the frame, thus if your frame is moving the same velocity as the frame of the particles in free space, the particles are not moving at all, or they are moving with speeds relative to the particle who's velocity is equal to yours). The 'temperature' would change if your frame velocity changed relative to that of the particles (think of a basic mechanical KE of 1/2mv^2). The final v is the difference in the v of your frame to the v of the particle frame. Temperature is a relative measure of the transfer of momentum from a system to its surroundings in a way.

Note that this is a very much simplified explanation, as this is not taking into account relativity. Also, in a gas or liquid, you would compare your frame velocity to the velocity of the averaged v vector of the system, in which case you will get your average temperature relative to your frame (look at friction welding to see a physical example of how momentum can translate into temperature)

https://www.youtube.com/watch?v=HVqJNax-Qzw