Thermodynamics In An Isolated System

[BOAS]

Hello,

I was thinking about a situation last night and couldn't convince myself of a correct answer, so I thought i'd put it to you guys.

Imagine an isolated system containing a star at some temperature radiating a given amount of energy into the environment. Can the environments temperature ever exceed that of the star?

I don't think such a situation would violate conservation of energy, because the star is converting mass into energy. But does this violate zeroth law?

My thoughts were that as the star radiates energy into the environment, it cannot escape and continues to build up due to the thermal radiation of the star. Given enough time, the system will reach thermal equilibrium, but can the environment exceed the temperature of the star at any point?

Thanks!

 

[Falcifer]

If we assume:
- The star and the environment are two separate systems, where heat is allowed to flow across their boundary.
- The initial temperature of the environment is less than that of the star.
- The star has a heat source, the environment has no heat source.

Then the environment will never have a temperature greater than the star until the two systems reach equilibrium. There also is nothing in this set-up that may suggest it could violate the zeroth law.

 

[Khashishi]

As the environment gets hot, the environment will start to glow according to the Stephan-Boltzmann law. When it reaches the same temperature as the star, the radiation from the star to the environment will equal the radiation from the environment to the star. Note that thermodynamics requires that the emissivity coefficient in the SB law equals the absorptivity coefficient.