Hot or cold, which wins

Slideways

I tried to google this but sorta failed.

Say for instance you have some metal plate, 300mm x 50mm x 25mm

You heat one plate to 100c and cool the other to -100c and place both in a room at 0c
Which one will reach room temp first and why? Only interesting if they don’t do it in sync of course

Cheers

mikhail

My thermodynamics doesn't go past a 1st year intro course, but I'd guess a simple model using the Stefan-Boltzmann law would describe the temperature radiated by both well enough for a first pass. It says the heat exchange is proportional to (Tp^4 - Te^4), where Tp is the temperature of the plate, and Te the temperature of the environment. Since they both start at the same absolute difference in temperature, the hot plate loses heat energy at the same rate as the cold plate absorbs it. Then the question is whether the relationship between change in heat energy and change in temperature is temperature-invariant, and that's where my recollection runs out. A quick google turned up this table, which suggests maybe it is since a single number is given for heat capacity of different metals without caveat.

Take the above with a healthy dose of salt. I know I passed that course, but I can't remember if it was by terribly much, and anyway, it's been a long time.

the_pen_turner

interesting question.
im going to say the hot one cools faster than the cool one heat up. several reasons . none of which could be factually corect

the hot one can loose the energy by any means, if some energy is lost through sound, light etc it still counts but the cool one can only absorb heat . the energy lost from the hot one thats not heat is no use to the cold one.

as the hot one cools is heats the room so its bringing the room temp closer to its own temp so shortening the diference needed but extending the diference the cool one has to change to reach room temp. this my be counter acted by my first point not sure

i think the type of metal would matter a lot. if the material has used extra energy changing states solid to liquid ect then that would play a big facter as they change back

Slideways

That’s two really interesting answers, thanks for taking the time.