What is the temperature after 4 hours? after 5 hours? how long before the temperature is below 90º?

Question

Coffee is poured at 142ºF into a travel cup. After 25 minutes in a 70º room the coffee has cooled to 139ºF. I accidentally left the coffee on the counter when I left. What is the temperature after 4 hours? after 5 hours? how long before the temperature is below 90º?

Show your process.

Answer 1

Hi Alyssa H.,

Like your other problem posed tonight, this is an "exponential decay" situation. The temperature of the coffee is decreasing like an exponential decay, from its original value to room temperature after infinite time. Set up your "calibration" equation to find the rate constant, and then apply it at the stated times elapsed.

-- Cheers, --Mr. d.