Homework SourseA freshly brewed cup of coffee has a temperature of 100 degr
A freshly brewed cup of coffee has a temperature of 100 degree C and is placed in a room at 15 degree C. After 30 minutes, the coffee has cooled to 65 degree C.
a. How long will it take for the cup of tea to cool to 20 degree C?
b. How fast is the temperature changing at the moment the temperature is 20 degree C?
a. How long will it take for the cup of tea to cool to 20 degree C?
b. How fast is the temperature changing at the moment the temperature is 20 degree C?
Solution
Formula for cooling:
T(t) = R + (T0 - R)e-kt
where R is room temperature, T0 is the initial temp, and k is an unknown constant.
T0 = 100
R = 15
T(t) = 15 + 85e-kt
T(30) = 65 = 15 + 85e-30k
k = (-1/30)ln(50/85) = 0.0177
T(t) = 15 + 85e-0.0177t
T(t) = 20 = 15 + 85e-0.0177t
a) t = (-1/0.0177)ln(5/85) = 160.1807 min
b) dT/dt = -0.0177(85e-0.0177t) = -0.0177(85e-0.0177(160.1807)) = -0.0883 degrees/min
