Why does heat transfer occur at a faster rate at lower temperatures?

[MOTO]

Hi all,

First of all I'm a hardware engineer and therefore my phisycs knowladge is quite limited...
Secondly my English is not well also so ... please forgive me.

I have a heat body (copper) which I want him to heat from -30C to +7C.

I supply it a constant power of let's say 7W (it has no matter for the discussion).

The phenomenan I see is that (delta T)/(delta t) at low tempertures is much higher then in high tempertures. I mean that for example the time that takes from -30C to -20C is much faster than the time from 0C to 7C.

a. What is the reason?
b. I need to have some algorithm that will keep a constant and linear (delta T)/(delta t) so that the time from -30C to -29C will be the same time (lets say 1 minute) as from -3C to -4C. What are the formulas I need to know in order to do it?

Thanks

 

[xiankai]

a. this may not be very technical but say, the temperature of the environment may also play a part in the heating factor?

b. you could probably that your heat body is heated in an enclosed environment (don't know the thermodynamic terms), since i think the specific heat capacity of copper doesn't vary with temperature, at least not with such a small range (at very high temperatures you may experience difficulty due to black-body radiation)

 

[Mentz114]

You need Newton's 'law of cooling' which states that the amount of heat transferred between system A and system B is proportional to their temperature difference.

\frac{dE}{dt} = K(T_a - T_b)

this accounts for the rapid transfer at low temperatures. It solves to an exponential for E(t).

 

[eaboujaoudeh]

yes actually the answer should take account both reasons..deltaT and the radiation emmissions which vary propotional to T^4 and that's a lot of difference with a small temperature change. and the surrounding temperature of the environment.