# Am I understand heat well?

Gold Member
I just thought about the following case and I have a doubt.
Say I have a system like this : B-------A-------B' where A is a continuously heated metal so that it's temperature remains constant with time. Imagine there's a fluid like air between A, B and B' so that A transfers heat to B and B' via convection. Suppose that the temperature of B is almost the one of A and the temperature of B' is much lower than the one of A. Suppose also that B and B' don't transfer heat to each other (because they are too far from each other).
Last supposition : B and B' are the same material, say a metal (whose specific heat is a constant).
My question is : If B get heated by 1K, does B' also get heated by 1K? I was tempted to say yes because they have the same specific heat but now I have doubts. I think that maybe B' can be heated more than 1K while B got heated by 1K, because the temperature of B is closer to the one of A than the one of B' is.
Maybe I should write down some equations, but I'll soon learn about gradient in cases similar to this one.
Thanks in advance.

## Answers and Replies

Mapes
Science Advisor
Homework Helper
Gold Member
My question is : If B get heated by 1K, does B' also get heated by 1K?

This question can't be answered unless you specific how the change in temperature occurs and how B and B' are being cooled. So far you've described a steady-state system where B-------A-------B' is symmetric up to a point; however, energy is being removed more rapidly from B' than from B (that's the only way to explain the difference in temperature of two identical materials).

Gold Member
This question can't be answered unless you specific how the change in temperature occurs and how B and B' are being cooled. So far you've described a steady-state system where B-------A-------B' is symmetric up to a point; however, energy is being removed more rapidly from B' than from B (that's the only way to explain the difference in temperature of two identical materials).

Ok I understand. I precise : the change in temperature occurs by convection due to air between A and B, and A and B'. And initially B and B' have different temperature. For example B and B' could have been cooled/heated in another systems and then put in the one I described.
I realize that if B is heated by 1K then B' will be heated by more than 1K. However I don't know why since they have the same specific heat.
Why does B receive less energy from A than B' does? Because of the slight difference of temperature?
My question is also equivalent to ask why a very hot body in air loses its heat quickly and then less and less quickly.
Is it because of the gradient of temperature? Newton's law of cooling? Are they (Newton law of cooling and the gradient) related?
I don't understand why the process of change of temperature works like it works.
By the way thanks for helping me.

Mapes
Science Advisor
Homework Helper
Gold Member
OK, got it. The general principle is that energy moves down a steeper gradient faster. Well, actually energy is moving everywhere all the time, but it's unlikely for it to move from a colder to a hotter material (Second Law). The unlikeliness increases with increasing temperature difference. So as a gradient increases, energy transfer down the gradient becomes more and more favorable, which translates into an increasing transfer rate. Yes, this is the origin of Newton's cooling and Fourier's conduction laws.

Gold Member
OK, got it. The general principle is that energy moves down a steeper gradient faster. Well, actually energy is moving everywhere all the time, but it's unlikely for it to move from a colder to a hotter material (Second Law). The unlikeliness increases with increasing temperature difference. So as a gradient increases, energy transfer down the gradient becomes more and more favorable, which translates into an increasing transfer rate. Yes, this is the origin of Newton's cooling and Fourier's conduction laws.

Thank you very much for the good explanation.