# Newton's Law of Cooling Problem--help please

• Apr 28th 2008, 09:43 AM
coe236
Newton's Law of Cooling Problem--help please
Hi,
here's the problem: A murder victim is discoverd in a sealed room w/thermostat set to 70 degrees. At 2PM the medical examiner finds the temperature of the body is 84.3. At 3PM the body temp is 77.15. Asuming that the victim had body temp 98.6 at the time of death and after death the body cooled according to Newton's Law of cooling, at what time did the victim die?
a) 9AM b)11:30AM c)12:30 d)1PM e)1:30PM

I'm kind of clueless on how to start except writing down the equation for newtons law: http://www.ugrad.math.ubc.ca/coursed...fs/cool_17.gif I'll appreciate any help, thankyou.
• Apr 28th 2008, 10:02 AM
Jameson
Quote:

Originally Posted by coe236
Hi,
here's the problem: A murder victim is discoverd in a sealed room w/thermostat set to 70 degrees. At 2PM the medical examiner finds the temperature of the body is 84.3. At 3PM the body temp is 77.15. Asuming that the victim had body temp 98.6 at the time of death and after death the body cooled according to Newton's Law of cooling, at what time did the victim die?
a) 9AM b)11:30AM c)12:30 d)1PM e)1:30PM

I'm kind of clueless on how to start except writing down the equation for newtons law: http://www.ugrad.math.ubc.ca/coursed...fs/cool_17.gif I'll appreciate any help, thankyou.

Well the solved differential equation for Newton's Law of Cooling is:
$T(t) = T_a + (T_0-T_a)e^{-kt}$, where Ta is the outside temperature and To is the original temp. If you want to see the derivation of this, check out this page.

Newton's Law of Cooling

Anyway, plug in your numbers into that equation and solve for your cooling constant, k. Once you have that you can solve for the total time the body has been cooling.