(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A copper sphere of radius d is put inside walls very close to 0K. The initial temperature of the sphere is [tex]T_0[/tex]. The surface of the sphere is totally black and we assume it loses energy only due to radiation.

1)Find an expression for the time passed till the temperature of the sphere decreases by a factor [tex]\eta[/tex].

2)Calculate explicitly t when [tex]\eta =2[/tex] and [tex]T_0 =300 K[/tex].

2. The attempt at a solution

I've found out http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html#c2.

So I searched for all the extra data I haven't been provided in the exercise, namely for the molar mass of copper, its density and the value of all the constants in the formula.

For part 1) I get [tex]t_{\eta}=\frac{mN_Ak_B (\eta ^3 -1)}{8M \sigma \pi d^2 T_0^3}[/tex].

For part 2), I used part 1) and plugged [tex]\eta =2[/tex], [tex]T_0=300[/tex] and I obtained [tex]t=891445d[/tex].

In all my arithmetics, I always used the SI units. So if d=1m, I get a time of [tex]891445 s>10 \text{days}[/tex] which seems to me way too long.

Further, if I double the radius of the sphere, it only double the time of cooling which doesn't seem right to me (I'd expect a 4 times bigger time of cooling), but I'm not 100% sure.

Am I doing something wrong? If not, what answer do you get?

P.S.: I used the density 8940 kg/m^3 and the molar mass M equal to 0.06354kg/mol.

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# Homework Help: Cooling of a sphere by radiation

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