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

Printable View

- Feb 24th 2009, 12:57 PMzangestu888Newtons 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, 01:58 PMskeeter
let y = temperature at any time t

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

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

$\displaystyle -1 = k(60 - 20)$

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

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

separate variables and solve for y as a function of t ... you have k and you also know y(0) = 90 - Feb 24th 2009, 02:17 PMzangestu888thanks!
thank you so very much for the help now i can conntiue!