Weight of Hot Body: Balance in Thermal Equilibrium?

[bernhard.rothenstein]

Consider a spherical hot body having a temperature T, located on one of the pans of a very sensitive balance. It is equilibrated puting a given mass on the other pan of the balance. The temperature T is lower then the ambiental one. The balance is in mechanical equilibrium but out of thermal equilibrium. Does the balance remain in a state of mechanical equilibrium when its temperature equates the ambiental one? The transmission of energy is isotropic.

 

[pervect]

The balance does not remain in a state of mechanical equilibrium - this follows from argments presented in

http://arxiv.org/abs/gr-qc/9909014

According to the general theory of relativity, kinetic energy contributes to gravitational mass. Surprisingly, the observational evidence for this prediction does not seem to be discussed in the literature. I reanalyze existing experimental data to test the equivalence principle for the kinetic energy of atomic electrons, and show that fairly strong limits on possible violations can be obtained.

It's also been discussed a lot here on the board, you can probably find the past discussions if you look.

Carlip's formula for "gravitational mass", the intergal of density + 3*pressure, is basically the flat-space version of the more general Komar mass formula which applies to any static metric.

 

[Entropia]

In this scenario, although the hot body and the balance are in mechanical equilibrium, there is a difference in temperature between them. This means that there is a flow of energy from the hot body to the balance, which will eventually lead to the balance reaching the same temperature as the ambient environment. As the temperature of the balance increases, it will experience a change in its properties, such as expansion or contraction, which may disrupt the mechanical equilibrium.

However, the transmission of energy in this scenario is isotropic, meaning that it is evenly distributed in all directions. This allows the balance to adjust to the changing temperature without any significant disruption to its mechanical equilibrium. As the balance reaches the same temperature as the ambient environment, the flow of energy will cease and the balance will remain in a state of mechanical equilibrium.

It is important to note that the balance may experience minor fluctuations in its weight as it adjusts to the changing temperature, but these fluctuations should not significantly impact its overall state of mechanical equilibrium. Overall, the balance should remain stable and in mechanical equilibrium even when its temperature equates the ambiental one, as long as the transmission of energy remains isotropic.