Newtons law of Cooling Q (1 Viewer)

[DistantCube]

Fitzpatrick Exercise 25(e) q4

A body initially at room temperature 20 degrees, is heated so that its temperature would rise by 5degrees/min if no cooling took place. Cooling does occur in accordance with Newton's Law of Cooling and the maximum temperature the body could attain is 120 degrees. How long would it take to reach a temperature of 100degrees.

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I searched the forum and this Q has already been asked, but no solution given, does anyone have the solution?

 

[serge]

should the temperature rise without cooling?
or do you need to take into account cooling while heating?

(this question is written really badly, plus by heating the object
chances are you're heating the surroundings, therefore the
room temperature will increase... I dont like it already)

 

[serge]

i have a new idea
taking time in minutes Temp in degrees

the dT/dt= -k(T-19) +5

5 degrees/ min being heated
and at a time 0 the object is T=20
where T= surroundings + Aekt

but t=20 and surroundings are 20? and ekt can never be 0
so i have no idea how to keep going, unless the question is wrong

 

[DistantCube]

That's my problem exactly, and without an expression for either A or k (which I also tried getting with Tmax=120, still nothing) I don't know how to solve it.

Also, from 25e I'm having trouble with Question 6b

 

[richz]

6b) V=A(1-e^(-kt))

.25V is filled, so A = 0.25V t=5

find value of k

then just sub in t = 10 to eqn, get the fraction and minus 0.25

 

[serge]

That's my problem exactly, and without an expression for either A or k (which I also tried getting with Tmax=120, still nothing) I don't know how to solve it.

I think if you pretend room temp is like 1 off...
say 19 degrees, then Ae^ok can=1 making A=1?
then you can get a close estimate...
if you want it correct to more decimal places then you
could say room temp is 19.99 degrees and A=0.01

I think then you could use the equation i typed up at the top

Apart from this being technically wrong
what do you think?

 

[richz]

well if u read the start of the exercise it says to use eqn T=P+Ae^(-kt)

 

[serge]

i dont have the book...
so im working with what distantcube wrote

either way, how's that gonna help if
both room temp and object temp is the same?

that way T= P +Ae-kt
T=P A=0 which it cant be since ekt greater than 0 at all times

 

[serge]

Newton's Law of cooling relies on the fact that
the object never reaches room temp...

Either Distantcube messed up... or this question is stupid

 

[richz]

i was talking to distant cube...........

 

[serge]

backwards! brilliant

close enough for me, lol

goodwork, couldnt figure out how it made sense
thanks for the explanation

the question says cooling happens aswell as heating...
so when you assume the T=25 at t=1, its not completely correct
I think that's why your answer is a little bit off

 

[DistantCube]

The question is typed exact. I think it's just a retarded question. Not anything youd get in the HSC anyway, I hope.

Thanks for 6b xr...