# Heat transfering issue

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.