# how hot is the oven?

• February 21st 2011, 05:12 AM
slapmaxwell1
how hot is the oven?
A thermometer reading 70 F is placed in an over pre-heated to a constant temperature. through a glass window in the over door, an observer records that the thermometer reads 110 F after 1/2 minute and 145 F after 1 minute. so how hot is the over..?

ok i have the formula for the problem,

dT/dt = k(T-Tm)

I also know that the initial temp is 70 F

I guess my problem starts with, not knowing how to separate the variables...any help would be appreciated.

• February 21st 2011, 05:16 AM
Ackbeet
Your k will be negative if you write the DE that way, but that's fine. You separate the way you always do:

$\dfrac{dT}{T-T_{m}}=k\,dt.$

Integration yields what?
• February 21st 2011, 09:51 AM
slapmaxwell1
integration yields T(t) = Tm +C*exp^(kt)

solving the problem T = 390 degrees...thanks!
• February 21st 2011, 10:14 AM
Ackbeet
Yep, that's what I get as well. You're welcome!