Newton's Law of Cooling

[alyren]

A thermometer reading 34 degree F is brought into a room with a constant temperature of 70 degree F. if the thermometer reads 40 degree F after 5 minutes, what will it read after bring in the room for 8 minutes?

Newton's law of cooling

U=T+(Uo-T)e^(kt)

is the right equation i set up?
40=70+(34-70)e^(5k)

i solved it and got 67.98 degree F as an answer

 

[mmm4444bot]

Newton's law of cooling

U = T + (Uo - T) e^(kt)

is the right equation i set up?

40 = 70 + (34 - 70) e^(5k) Yes, this looks correct.



i solved it and got 67.98 degree F as an answer

That seems too high.

The reading increased six degrees over the first five minutes.

You're saying that it increased about 28 degrees over the next three minutes.

Since the room temperature is constant, there's nothing to speed up the thermometer's rate of increase.

The reading should be less than 50 degrees, I think.

Please show your work.

For example, what value did you get for k ?

Have you been previously asked to show your work ?

 

[alyren]

40=70+(34-70)e^(5k)

k =-0.36

then

U=70-36e^(-0.36*8)
=67.98

 

[mmm4444bot]

k = -0.36

That value is about 10 times bigger than what I get:

k = -0.03646 (rounded)

I cannot see your work, so I can only suggest that you check your arithmetic.

 

[alyren]

ok i got it, -0.36 is what i did wrong, it should be -0.036. i got 43 degree F as an answer.