# Newton's law of cooling

## Homework Statement

A hot metal rod is placed in a water bath whose temperature is 40F. The rod cools from 300F to 200F in 1 minute. How long will it take for the rod to cool to 150F?

## The Attempt at a Solution

I know y'=-k(y-T0)
and y(t) = T0 + Ce^-kt
and i also know that's not much of a start...

Mark44
Mentor
What you show as your attempt are actually the relevant equations. The first is the differential equation that relates the rate of cooling (y'(t)) to the temperature y(t). The second equation is the general solution to the differential equation.

How the solution is gotten from the differential equation might be more advanced than you can understand right now, so what you need to do is use the given information about the temperatures at the two times to find the parameters T0, C, and k. Then you will be able to use the formula to calculate the temperature at any time t.

Some questions for you:
What does T0 represent?
At what time is the rod's temperature 300 degrees F?
At what time is the rod's temperature 200 degrees F?

Use the formula for temperature to write equations involving the information above and solve for C and k, then use your formula to find the time at which the rod has cooled to 150 deg. F.