# Thread: Temperature of a conductor equation

1. ## Temperature of a conductor equation

If anyone can help me out with this it will be much appreciated.

The temperature of a conductor at time, t, is given by:

Where is the initial temperature and T is a constant

Express T in terms of , , and t and determine its value when = 190, = 20 and t = 40.

2. This doesn't really belong in "Linear and Abstract Algebra", it is just a matter of basic algebra.

From $\displaystyle \theta= \theta_0\left(1- e^{\frac{t}{T}}\right)$ you can divide both sides by $\displaystyle \theta_0$ to get $\displaystyle \frac{\theta}{\theta_0}= 1- e^{\frac{t}{T}}$. Now add $\displaystyle e^{\frac{t}{T}}$ to both sides and subtract $\displaystyle \frac{\theta}{\theta_0}$ from both sides to get $\displaystyle e^{\frac{t}{T}}= 1- \frac{\theta}{\theta_0}$

Take the natural logarithm of both sides to get
$\displaystyle \frac{t}{T}= ln\left(1- \frac{\theta}{\theta_0}\right)$

Can you finish it from there?

3. Yes I can, thank you.