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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.

Help me, please!

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

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# Newton's Law of Cooling

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