# Cooling a ball of iron

Tags:
1. Sep 21, 2015

### alivedude

1. The problem statement, all variables and given/known data

A boll of iron with the volume $V=\frac{4 \pi 0.01^3}{3}$ heats up to 1073 K in a chamber with vacuum, how long will it take until the iron is at 1063 K? The given data is this:
$\rho_{iron} = 7870 kg/m^3$
specific heat.. $c_i = 0.5 \cdot 10^3 J/(kg \cdot K)$

2. Relevant equations
Newtons law of cooling: $T(t)=(T_1-T_0)e^{-\frac{k}{c}t}+T_0$

3. The attempt at a solution

Im stuck with that $k$ in the exponential. I know how to use the differential equation but i can't solve for $t$ as long as i have that unknown $k$ there, right? Can I approximate it or something?

Can I do something else? Since they give me the volume and density I'm thinking that maybe i should go with some other approach?

2. Sep 21, 2015

### Staff: Mentor

Newton's law of cooling does not apply in a vacuum. How does energy transfer happen in a vacuum?

3. Sep 22, 2015

### alivedude

Ofc, don't know what I was thinking. But hey, then I could just calculate the amount of heat needed to lower the temp. by 10 K and then use Stefan Boltzmanns law to solve for $dt$ right? Can I approximate it for a black body?

4. Sep 22, 2015

### alivedude

The problem is solved! :)