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Afaik. temperature is in relation with the kinetic energy of the individual molecules. In vacuum there are only a few molecules so measuring their kinetic energy is very hard, because vacuum has a very little heat capacity and the thermometer with much higher heat capacity will interfere with measurement. I guess the heat transport will be slow too, because heat conduction and convection will be negligable and only heat radiation will transport energy between the wall of the vacuum container and the thermometer. Is there a better way to measure temperature in vacuum?

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The temperature of a true vacuum would be a measure for the energy distribution of the photon gas in that vacuum. You can derive the occupation of the electromagnetic modes in a volume with Bose-Einstein statistics, which is essentially what Planck did to describe the emission spectrum of a black body.

However, you don't need to do understand the details of this derivation, because the photon gas will be in thermal equilibrium with the vessel walls. So, stick a thermometer with a high-emissivity surface (e.g., glass) in the vacuum vessel and wait until it has equilibrated with the walls by radiative energy exchange.

This will even work if the walls are very far away, or not there at all, like in outer space. The thermomemeter has temperature $T_t$ and will radiate with a flux $\sigma T_t^4$, where $\sigma$ is the Stefan-Boltzmann constant; at the same time, it will receive a flux $\sigma T_e^4$, where $T_e$ is the temperature of the photon gas in vacuum. The temperature of the thermometer will gradually approach the temperature of the photon gas.

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  • $\begingroup$ Is there a way to measure the temperature directly on the vacuum and not on the walls? E.g. how do we measure it in the space, where there are no walls? :-) $\endgroup$ – inf3rno May 29 '16 at 12:14
  • $\begingroup$ Updated answer. $\endgroup$ – Han-Kwang Nienhuys May 29 '16 at 12:21
  • $\begingroup$ And be careful to isolate your vacuum vessel from radiation coming from the outside environment! $\endgroup$ – valerio May 29 '16 at 13:17
  • $\begingroup$ @valerio92: huh? Under what circumstances would that result in the temperature measured inside the vessel to be different from the "true" temperature of the vacuum? $\endgroup$ – Han-Kwang Nienhuys May 29 '16 at 13:32
  • $\begingroup$ I just wanted to point out that if the walls are non-adiabatic they will eventually thermalize with respect to the outside environment, so you will be actually measuring the temperature of the outside environment. But you are right, the mechanism would still be the same and you still would be measuring the temperature of vacuum, so maybe my observation was useless. Just wanted to point out that the "temperature of vacuum" in a vessel would depend on the outside environment unless the walls are adiabatic. Peace! $\endgroup$ – valerio May 29 '16 at 14:08

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