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

• September 7th 2007, 04:19 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!!!!!!!!!!!
• September 7th 2007, 09:07 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
• September 7th 2007, 09:23 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:

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

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

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

RonL