find temp

**Morgan82** · Dec 3rd 2009, 07:00 PM

A pan of water (46 degrees) was put into a fridge. Ten min. later, the temp was 39; 10 min. later, the temp was 33.
Use newtons law of cooling to find the temp of the fridge..
I know the equation.

Do I need to find the rate, or how do I do this?

**nehme007** · Dec 3rd 2009, 08:16 PM

By Newton's law of cooling you have that the temperature of the water is given by:
$T(t) = T_f + (46 - T_f) e^{-rt}$
where $T_f$ is the temperature of the fridge and r is some unknown rate constant. You are told T(10) = 39 and T(20) = 33, so:
$T(10) = 39 = T_f + (46 - T_f) e^{-10r}$
$T(20) = 33 = T_f + (46 - T_f) e^{-20r}$
The first equation gives you:
$r = -1/10 ln(\frac{39-T_f}{46 - T_f})$
and the second gives you:
$r = -1/20 ln (\frac{33-T_f}{46 - T_f})$ .
Equating these two expressions for r and multiplying by -20 yields:
$2ln(\frac{39-T_f}{46 - T_f}) = ln (\frac{33-T_f}{46 - T_f})$ .
The 2 can move inside the log as a power, then you can get rid of the logs and solve. You should get $T_f = -3$ .

Thread: find temp

LinkBack

Thread Tools

Display

find temp

Similar Math Help Forum Discussions

differential temp coefficient

temp subject

private temp

Outside Temp Differential Equation

obtain rate of temp change

Search Tags