# Newton's law of cooling

Hey, I'm having problems with this question:

According to Newton's law of cooling, what cools faster, a person from 150 degress celcius to 100 degrees celcius or 100 degrees celcius to 50 degrees celcius in a laboratory environment? Why?

I' not really sure where to start.
I know the formula for this law is (T-Tr)= (To-Tr)e^-t/time constant

I guess wha I'm confused about is that I don't have some of the variables that I need like the time constant.

If anyone can point me in the right direction it would be much appreicated!

Thanks

## Answers and Replies

The information we get from the equation is that the rate of cooling depends only on the material involved and the initial temperature difference, and it sounds like the material (human) is the same in both cases!

Does this then mean that the body would cool at the same rate in both situations since they both have a temperature difference of 50 degrees celcius?

russ_watters
Mentor
It doesn't seem clear to me that the "laboratory environment" is 100C in the first instance and 50C in the second. Why can't it be 20C in both? It doesn't say.

Integral
Staff Emeritus
Science Advisor
Gold Member
Since the external temperature is not specified the only way to interpret the problem to make any sense is to a assume a constant lab temp.

I imagined that the first case had the person$$^1$$ at 150C, with the lab at 100C, and that the second case has the person$$^2$$ at 100C and the lab at 50C.

1. Steaming pile of ashes.
2. Boiling goo.

I imagined that the first case had the person$$^1$$ at 150C, with the lab at 100C, and that the second case has the person$$^2$$ at 100C and the lab at 50C.

1. Steaming pile of ashes.
2. Boiling goo.

I really doubt that the lab would be at 212 degrees fahrenheit.
The question is asking whether it takes longer to go from 150>>100 or from 100>>50 in an environment that is 20 degrees to start with.

Temperature loss occurs the faster at bigger differences, and slower when close to equilibrium.

thank you all for you help, I now have some ideas to work with!