# [SOLVED] Cal2 Integral Word Problem (finding average)?

• Jan 31st 2010, 08:36 AM
racewithferrari
[SOLVED] Cal2 Integral Word Problem (finding average)?
(a) A cup of coffee has temperature 95 C and takes 30 minutes to cool to 61 C in a room with temperature 20 C. Use Newton's Law of cooling system to show that the temperature of the coffee after t minutes is
T(t) = 20 + 75e^(-kt) where k = 0.02

(b) What is the average temperature of the coffee during the first half hour?
• Jan 31st 2010, 10:31 AM
skeeter
Quote:

Originally Posted by racewithferrari
(a) A cup of coffee has temperature 95 C and takes 30 minutes to cool to 61 C in a room with temperature 20 C. Use Newton's Law of cooling system to show that the temperature of the coffee after t minutes is
T(t) = 20 + 75e^(-kt) where k = 0.02

(b) What is the average temperature of the coffee during the first half hour?

(a) Newton's law of cooling says the rate at which a substance cools is directly proportional between the temperature of the substance and the temperature of its surroundings.

$\displaystyle \frac{dT}{dt} = -k(T - S)$

solve the differential equation for T using the given time/temp data.

(b) $\displaystyle T_{avg} = \frac{1}{t_2 - t_1} \int_{t_1}^{t^2} T(t) \, dt$
• Jan 31st 2010, 11:54 AM
racewithferrari
can tell me what is the value of T and S and how what values to be put in the equation

Thanks
• Jan 31st 2010, 01:18 PM
skeeter
Quote:

Originally Posted by racewithferrari
can tell me what is the value of T and S and how what values to be put in the equation

Thanks

S = 20 ... T is a variable