upper o lower vaule for the constant, k in newt law cooling

• Sep 7th 2007, 03:19 AM
zena
upper o lower vaule for the constant, k in newt law cooling
I have asked a similar question before but i realised i was asking the wrong thing...........

a. for the equation dT/dt= -k(T-8) what is the upper or lower limit of k if the temperature (T) is to never fall below T=15 ......... when t=0, T=16

b. if k=0 what does this say about the insulation properties of k? :rolleyes:

THANK YOU!!!!!!!!!!!
• Sep 7th 2007, 08:07 AM
CaptainBlack
Quote:

Originally Posted by zena
I have asked a similar question before but i realised i was asking the wrong thing...........

a. for the equation dT/dt= -k(T-8) what is the upper or lower limit of k if the temperature (T) is to never fall below T=15 ......... when t=0, T=16

b. if k=0 what does this say about the insulation properties of k? :rolleyes:

THANK YOU!!!!!!!!!!!

if I recall correctly.

RonL
• Sep 7th 2007, 08:23 AM
CaptainBlack
Quote:

Originally Posted by zena
I have asked a similar question before but i realised i was asking the wrong thing...........

a. for the equation dT/dt= -k(T-8) what is the upper or lower limit of k if the temperature (T) is to never fall below T=15 ......... when t=0, T=16

b. if k=0 what does this say about the insulation properties of k? :rolleyes:

THANK YOU!!!!!!!!!!!

First solve the differential equation.

In this case the solution is:

$\displaystyle T=8(1+e^{-kt})$

so when $\displaystyle t=0,\ T=16$, and if $\displaystyle k>0$ as $\displaystyle t \to \infty\ T \to 8$.

Hence for all $\displaystyle k>0$ the temprature eventualy drops below 15.
If $\displaystyle k \le 0$ the temprature never falls below 16.

RonL