Does temperature diffuse between two objects at a constant rate or does the difference in temperature determine the rate?
For example, you place two cans of coke in a 35 degree refrigerator. One can is 95 degrees and the other is 40 degrees. Will their temperatures lower at the same rate or will the hotter can diffuse more rapidly?
In: Physics
This actually depends how technical you want to be.
The rate of energy transfer between the objects is the same (thats conservation of energy) and is done by the equation Q (energy transfer/change) = m (mass) * cp (heat capacity) * dT (difference in temperature between the two objects.
So if the two have the same mass and are made of the same thing (m and cp) then they change temperature at the same rate. And if not they don’t.
If you want to be super super picky technically cp is dependent on temperature, so they go at slightly different rates, though the scale difference has to be pretty huge for the number the change enough to change the answer. The an equation is used to figure out a new CP at a given temperature for a specific compound.
This also changes if one undergoes a phase change (like ice to water) in which case it will absorb the energy but rather than use that energy to change T it will use it to break the structure down, so it will stay at one temperature while the other drops.
Edit: and if you want to be super super super picky then the above is assuming its not losing heat to the surrounding air, in reality the hot one would lose heat more quickly to the air (with the same equation) so would drop slightly faster because it is losing heat to both places.
Edit2: I’ve forgotten the name of the equation and I thought it was the Arrhenius equation but thats slightly different, sorry its been a while since phys chem
EDIT3: it has been correctly pointed out that the Arrhenius equation is actually the right one for calculating the thermal conductivity of a substance, thats me being sleepy and I apologize. I’m leaving the above as is though because I think it hits on the key points around what determines how much energy is lost from a thing when next to another thing of a different temperature and probably addresses OPs concerns and follow up questions.
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