Timeline for Relativity of temperature paradox
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2016 at 13:54 | comment | added | WillO | @ArnoldNeumaier: Thank you. I think the phrase I needed to hear was "due to the frame dependence of the volume that enters the thermodynamics". | |
| Jun 23, 2016 at 13:40 | comment | added | Arnold Neumaier | No molecular model is needed, the equations for fluid mechanics date from 160 years ago, long before a molecular interpretation of temperature existed. Of course the results are invariant under Galilei boosts. The conceptual problems arise only in the relativistic regime, due to the frame dependence of the volume that enters the thermodynamics. For a nonrelativistic ideal monatomic gas, your formula is correct. | |
| Jun 23, 2016 at 13:40 | comment | added | Arnold Neumaier | The temperature reported by the weather bureau is the one modelled with (Galilei invariant) nonrelativistic fluid mechanics in the rest frame of the Earth. On this level there are no conceptual problems, the temperature is a scalar field and the temperature at point x at time t is well-defined. Under the assumption that it doesn't change too rapidly in time and space it can be measured by placing a thermometer in a region of spacetime and wait until it equilibrates. What you read off from the Thermometer is the temperature. | |
| Jun 23, 2016 at 12:33 | comment | added | WillO | @ArnoldNeumaier: I take your point, but: The weather bureau does report an air temperature even on windy days, so I think it's fair to ask what they mean by that. In fact, they report a temperature and a wind chill factor separately, which suggests that the temperature should be frame-independent (because anything that depends on the wind velocity should be incorporated in the wind chill factor). If "temperature" means something frame-independent, I can't imagine what it could be other than the variance of velocity. (Of course there could still be measurement problems...). | |
| Jun 19, 2016 at 12:39 | history | wiki removed | Qmechanic♦ | ||
| Jun 18, 2016 at 17:54 | comment | added | WillO | @user929304: The speed of a particle is the norm of its velocity vector. The average speed of a particle is the sum of the speeds of all the particles, divided by the number of particles. The average velocity of a particle is the sum of the velocities of all the particles, divided by the number of particles. When it's very windy, the average velocity is high. When it's very cold, the average speed is low. | |
| Jun 18, 2016 at 17:25 | comment | added | user929304 | Thanks, I m not so sure about your last paragraph, i mean isn't speed just another name for the norm of the velocity vector? So when you speed minus velocity, i dont really understand. Would you a bit more clarity? | |
| Jun 18, 2016 at 15:21 | comment | added | Arnold Neumaier | The question is meaningful but whether they would show the same reading is not clear. Wouldn't the high-speed flow across the thermometer heat it up, and the amount depends on the relative speed and on how long the measurement takes? So it is questionable whether the temperature is meaningfully defined through such a measurement. | |
| Jun 18, 2016 at 14:58 | comment | added | WillO | @ArnoldNeumaier : But if two thermometers are in uniform motion with respect to each other when they both encounter the same cloud of gas, it still makes sense to ask whether they'll show the same readings --- and it seems to me that if the answer is yes, we'd want to call that a frame-independent measurement, no? | |
| Jun 18, 2016 at 14:45 | comment | added | Arnold Neumaier | what is measured by your thermometer is always measured in the rest frame of the thermometer. Thus it is meaningless to ask for a quantity that is frame independent, unless there are independent reasons for the latter. | |
| Jun 17, 2016 at 20:11 | history | edited | WillO | CC BY-SA 3.0 |
added 20 characters in body
|
| S Jun 17, 2016 at 20:06 | history | answered | WillO | CC BY-SA 3.0 | |
| S Jun 17, 2016 at 20:06 | history | made wiki | Post Made Community Wiki by WillO |