Question

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 185 degrees Fahrenheit when freshly poured, and 1.5 minutes later has cooled to 167 degrees in a room at 80 degrees, determine when the coffee reaches a temperature of 127 degrees.
The coffee will reach a temperature of 127 degrees in how many minutes?

Answer 1

= *(T-1) T=To trekt -Kt TC) = 185 , To = 80 185 = 80 + C C= 105 -kt T= 80 tlose Griller, T(1.5) =167 -1.5 167= 80 tlose -1.sk e - 87 - Tos K = 0.1253 -0.12530 T= 80 +105€ -0.12530 127. = so trose -0.12536 = 47 los t=6.41 min