# Homework Help: Newton's law of cooling and your body

1. Oct 24, 2009

### captainjack2000

1. The problem statement, all variables and given/known data
a body has temperature 27C at twelve oclock. The room temperature is constant at 16C. Two hours later the body was found to have a temperature of 24C. The temperature of a normal human body is 37C.Using Newton's law of cooling estimate the time of death.

2. Relevant equations
Newton's law of cooling says that the rate of heat loss from a body is proportional to the temperature difference between it and the surroundings.
dQ/dt=hA(Te-Tb)
where Te is the temp of the environment 16C=289K and Tb is the temp of the body 24C=297K. I am not sure what the heat transfer coefficient h is or how to determine this. Also not sure how to use the fact that normal body temperature is 37C

Could someone please give a bit of a start in the right direction
Thank you

2. Oct 24, 2009

### Staff: Mentor

Think of Newton's law of cooling in this form:
dT/dt = -k(T - Te)

What's the general form of the solution to that equation?

3. Oct 24, 2009

### jdwood983

After some googling, the heat transfer coefficient for an idle body is $$2.1 W/m^2\cdot K$$ and the approximated surface area is $$1.7 m^2$$.

As for solving this, you'd need to integrate your equation (which btw should be $$dT/dt$$, not $$dQ/dt$$ and find the temperature at a later time $$t$$ is

$$T(t)=T_a+\left(T_0-T_a\right)\exp[-hAt]$$

where $$T_a$$ is the ambient temperature and $$T_0$$ is the initial temperature of the body.