Newton's Cooling Extended Response Q's

[danieltennis]

Hey,

I have an analysis SAC that goes for three double periods and my teacher said that the first part is going be based on Newton's Cooling and differential equations. I was wondering if anyone can post up any extended response relating to Newton's Cooling or refer me to an trial exam, a resource or a textbook. I done most of the questions in the Heinemann textbook.

Thanks for your help guys,

Daniel

[monokekie]

TT told me there's an example question in chapter 9 about this.... and that's all i had done  =S

[/0]

A corpse is discovered at 12:30am, and is found to be , while the temperature of the night air is

a) Write down a differential equation for the body temperature at time t hours after 12:30am.

An hour later, the coroner arrives and measures the body's temperature to be

b) Solve the equation in a), expressing T as a function of t.

c) A suspect tells police that he had seen the person alive and well at 11:00pm. Knowing that normal body temperature is , what is wrong about the story? Why?

d) Given the evidence, what is the predicted time of death?


ANS:
a) dT/dt = k(T-5)
b) T = 5(3/5)^t+5
c) Body temperature would be 15.8 degrees celcius at 11pm.
d) 8:52pm
(edited)

ALSO TRY TSFX 2006 Exam 2 for a devilish cooling problem

[danieltennis]

Awesome! Thanks /0

You wrote these questions?

[d0minicz]

can soemone show me their workings for part b)
thanks

[TrueTears]

Awesome! Thanks /0

You wrote these questions?

No it's from our SAC.

[d0minicz]

can soemone show me their workings for part b)
thanks

oops dont worry realised i copied soemthing down wrong lol

[/0]

Awesome! Thanks /0

You wrote these questions?

No it's from our SAC.

No it's based on a practice sac

[/0]

1. It's not from our actual SAC, it's from practice SAC
2. It is not copied word for word

[TrueTears]

1. It's not from our actual SAC, it's from practice SAC
2. It is not copied word for word

Ofcourse it's not copied word for word after you edited it.

[Mao]

1. It's not from our actual SAC, it's from practice SAC
2. It is not copied word for word

Ofcourse it's not copied word for word after you edited it.

« Last Edit: August 18, 2009, 09:48:15 PM by /0 », before the time of your post « Reply #5 on: August 18, 2009, 10:15:34 PM »

[kat148]

VCAA 2003 Exam 2 Question 5b)

http://en.allexperts.com/q/Calculus-2063/Newton-law-cooling-growth.htm
http://answers.yahoo.com/question/index?qid=20070206171629AA8cYAQ

(not sure if these are reliable/related to study design)

[danieltennis]

Wait, shouldn't the solution to a) be dT/dt =k(T-5) not dt/dT =k(T-5)?

[Mao]

Wait, shouldn't the solution to a) be dT/dt =k(T-5) not dt/dT =k(T-5)?

no, Newton's Law of Cooling states the rate of change of temperature is proportional to the temperature difference, hence the rate is dT/dt, how temperature changes as time changes.

The inverse, dt/dT is how time changes as temperature changes, which doesn't really make much sense.

[kat148]

Found a question ganges posted last year:

A theremometer is taken from a house at 21 degrees to the outside. One minute later it reads 27 degrees, another minute later it reads 30 degrees. find temperature outside house.

answers like 33 degress, how?

Mao's solution