Newtons Law of Cooling

• Feb 24th 2009, 01:57 PM
zangestu888
Newtons Law of Cooling
A cup of coffee was prepared at 90 degree C and left in a room at 20 degree C. Now the temperature is 60 degree and it is cooling at 1 degree/min. How much time has past since the coffee was made.
? netwons law ? dont know how to start it :S
• Feb 24th 2009, 02:58 PM
skeeter
let y = temperature at any time t

$\frac{dy}{dt} = k(y - 20)$

at $y = 60$ degrees, $\frac{dy}{dt} = -1$ deg/min

$-1 = k(60 - 20)$

$k = -\frac{1}{40}$

$\frac{dy}{dt} = k(y - 20)$

separate variables and solve for y as a function of t ... you have k and you also know y(0) = 90
• Feb 24th 2009, 03:17 PM
zangestu888
thanks!
thank you so very much for the help now i can conntiue!