How Do You Calculate Initial Temperature Using Newton's Law of Cooling?

[luigihs]

A hot object cools down to a temperature of 10 degrees of Celsius during a period of 180 seconds. The room temperature is 10 degrees of Celsius. Assume the coefficient in the Newton's Law of cooling to be 0.01[1/sec]. Determine the original temperature of the substance



2. T(room) + (T(initial) T(room)) e^-kt = T(final)

t room = 10
ti = ?
Tfinal = 10

3. 10 + (Ti -10 ) e^(-0.01)(180) = 10
10 + Ti - 10 + 0.1652 = 10
0.1652 = 10 = 60.53

I think this wrong because its a multiple choice and the choices are 93 and 100

Please help me thank you!

 

[Spinnor]

Shouldn't T final be a little above room temperature? Anyway a problem similar to this is done here,

http://ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

See example 1.

Also you could plug in your possible answers and see if they work, I don't think they will as I think your initial data is off?

 

[luigihs]

Shouldn't T final be a little above room temperature? Anyway a problem similar to this is done here,

http://ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

See example 1.

Also you could plug in your possible answers and see if they work, I don't think they will as I think your initial data is off?

:( Sorry I still struggling with the problem, can you please show me how to do ? please!

 

[Spinnor]

You wrote,

"10 + (Ti -10 ) e^(-0.01)(180) = 10"

Subtract 10 from both sides and we have,

(Ti -10 ) e^(-0.01)(180) = 0 --> Ti = 10The object did not cool down to room temperature in 180 seconds unless it started at room temperature. I think your facts are wrong. Assume that 100 was the starting temp and work backward to find the final temp, which can't be 10.Tf = 10 + (100 - 10)*exp(-1.8) Tf = 24.9

Tf = 10 + (93 - 10)*exp(-1.8) Tf = 23.7

Good luck!

You might also visit,

http://demonstrations.wolfram.com/NewtonsLawOfCooling/

 

[fahanaam]

sorry, what is the ambient temperature? I've assignment where the question as follow:

the temperature T of a cooling object drops at a rate proportional to the difference T-S, where S is constant temperature of surrounding medium. If initially T= 100 C, find the temperature of the cooling object at any time. anyone...please help me..

 

[LawrenceC]

fahanaam, refer to the rules of this forum.