Total energy required

1. Jun 10, 2010

Dafe

Hi,

a question at work popped up and it's been too long since I went to school :p

The total energy [Wh] required to heat the system to temperature T is given by f(T)=1.28T. The effect [W] applied to the system is given by g(T)=378-3.16T. How long does it take to heat the material to say 80 degrees?

Hope someone can help me out, thanks.

2. Jun 10, 2010

Dafe

Here's my try. I'm using wolframalpha for the differentiation and integration...

$$\frac{dh}{dT}=\frac{d}{dT}\left(\frac{f(T)}{g(T)}\right)$$

$$=\frac{d}{dT}\left(\frac{1.28T}{378-3.16T}\right)$$

$$=\frac{4.04T}{(378-3.16T)^2}+\frac{1.28}{378-3.16T}$$

So now I have the change in time required to heat up the material as a function of temperature. I integrate to get the time required:

$$h(T)=\frac{153.1}{378-3.16T}$$

Meh, at least it's an attempt :p