# Newton's Law of Cooling

1. Apr 11, 2006

### Chubbly

Hello,

I am an undergrad student studying Physics.

We are currently studying thermodynamics. The lecturer has set us a bunch of problems relating to Thermodynamics. While I can do most of them, I am getting completely thrown by one question:

An object with a surface area of 0.2 m², an emissivity of 0.8 and a heat capacity of 1320.0 J/K has a temperature of 59.0 °C. It is then place in an environment at 38.0 °C and it eventually cools until it is in thermal equilibrium with the new environment.

Stefan constant: σ = 5.68 x 10-8 W m-2 K-4
Coefficient of convective heat transfer = 6.0 W m-2 K-1

Approximately how long does the object take to cool to a temperature 14.0 K below its initial temperature?

The lecturer has said that Newton's Law of Cooling can be assumed to be valid. So I dug up the approximation of Newton's Law of Cooling which is, as I understand it:

dT/dt=(A/C)(q+εσ(Tave)^3) ∆T

or, in words

rate of change in temperature with respect to time = (surface area/heat capacity)(Coefficient of convective heat transfer + emissivity*Stefan's constant*average temperature cubed)*change in temperature.

The working
I'm sorry it's so messy, its hard to put a complicated formula in word characters.

dt=dT/((A/C)(q+εσ(Tave)^3) ∆T)

dT=59+273.16
A=0.2
C=1320
q=6
ε=.8
σ=5.68 x 10-8
(Tave)^3=((59+(59-14))/2+273.16)^3=34378849.96
∆T=14

It seems like a basic number plugger but every time I put the values in, it's wrong.

I tried unit cancellation to check, I tried all manner of different forms of the values but nothing works.

(the answer is given, and it's 220s)

2. Apr 11, 2006

### siddharth

These sites covers it pretty well