SOLUTION: 1. Newtons law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At th

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 1. Newtons law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At th      Log On


   

Question 42108: 1. Newtons law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At the moment a steel plate at 270 degrees C is placed in air that is at 20 degrees C, its rate of cooling is 50 degrees C per minute. How fast is it cooling when the plate temperature is 100 degrees C?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate of cooling = Q degrees/min., temperature of the plate = T%5Eo C, temperature of surrounding air = t%5Eo C.

According to given condition:
Q+=+k%28T-t%29 _________(1)
where k = constant of variation.
When T = 270, t = 20, Q = 50.
Putting these values of T, t and Q in (1) we have
50=k%28270-20%29
or k+=+50%2F220 = 5%2F22

Substituting this value of k in (1) we have
Q+=+%285%2F22%29%28T-t%29 _________(2)

When, T = 100 and t = 20 [assuming temperature of surrounding air remains constant] then from (2),
Q+=+%285%2F22%29%28100-20%29
or Q+=+%285%2F22%2980 = 200%2F11 = 18.18 (approx)

Hence, reqd. rate of cooling is 18.18%5Eo per minute.