newton's law of cooling states the temperature of a body at a time t after being introduced into an environment

Question

Newton's law of cooling states the temperature of a body at a time t after being introduced into an environment having constant temperature T_o is A(t)=T_o+Ce^-kt, where C and K are constants and t is in minutes.If C=100 and K=.1, how long will it take a cup of coffee to cool to a temperature of 25^oC if it is in a room that is 20^oC.

Answer 1

This question just requires that you plug the numbers you're given into the equation. C = 100, k = 0.1, and T₀ = the room's constant temperature of 20ºC. You want the coffee's temperature to cool to A(t) = 25ºC. Plug in and solve for t:

 

25 = 20 + 100e^-0.1t

5 = 100e^-0.1t

0.05 = e^-0.1t

ln(0.05) = -0.1t

-3.0 = -0.1t

t = 30.0

 

It will take the cup of coffee 30 minutes to cool to 25ºC.