A cup of coffee that has an initial temperature of 280degree

A cup of coffee that has an initial temperature of 280degree is brought to class which is kept at 72degree. After 10 minutes, the coffee cools down to a temperature of 2.44degree. a) Write the function that represents the temperature of the coffee at any time, x, beginning with the time the coffee was brought to class, b) How long will it take the coffee too cool to 2OOdegree?

Solution

solution:

assuming the coolinng rate is linear

and cooling rate constant is k

hence at any time t

the temperature of cofee is given as

T=280-72kt

now at t=10, T=244

hence

244=280-720k

720k=36

k=1/20

hence

T=280-72t/20

T=280-3.6t

b)

now for T=200

200=280-3.6t

80=3.6t

t=80/3.6=22.22 min