## Heat stuff (3)

### 1 Name: Mad Scientist 2005-10-08 15:22 ID:n9PP0aN1

Okay, I have a very textbook-y question here (no, this isn't for a school problem). I've got two objects, one with a volume of 0.002 cm^3, specific heat of about 1.75, and a temperature of about 1200 C. The second object is around 35 C, a volume of about 0.5 cm^3, and a specific heat of around 2. The interface between the materials is 0.01 cm^2. Any way I can find out what temp the two equalize at, and the temp as a function of time (for the second object)? Sorry for the extremely boring problem, but I need to know.

### 2 Name: Mad Scientist 2005-10-09 23:09 ID:FqNkEwdi

If T is the the temperature bot objects equalise at (assuming perfect insulation, m=mass, c=specific heat)

m1*c1*(T1-T) = m2*c2*(T-T2)
<=>
T = (m1*c1*T1 + m2*c2*T2)/(m1*c1 + m2*c2)

If densities aren't radically different T should be about 40°C.

>Any way I can find out what temp the two equalize at, and the temp as a function of time (for the second object)?

There is no eay answer for that. You could try an (very) rough estimate using Newton's law of cooling :

T(t) = 40°C + (1200°C - 40°C)*exp(-k*t)

The problem is figuring out the constant k. You'd have to do at least one test run.

### 3 Name: Mad Scientist 2005-10-09 23:24 ID:FqNkEwdi

Gah, I can't read.
If you want the temperature of the second object that would be:

T(t) = 35°C + (1200°C - 40°C)*(1 - exp(-k*t))*m1*c1/m2*c2

But that's probably so inaccurate that it's useless.

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