Question

According to Newton's Law of Cooling, if a body with temperature T 1 is placed in surroundings with temperature T 0, different from that of T 1, the body will either cool or warm to temperature T(t) after t minutes, where:

T(t) = T 0 + (T 1 - T 0)e kt

and k is a constant.

A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≈ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes.

The temperature is about
degrees Fahrenheit.

Answer 1

We can substitute the given values into the equation for T, given the surrounding temperature T0 = 0, initial temperature T1 = 140, constant k = -0.0815, and time t = 15 minutes.

T = 0 + (140 - 0)e^(-0.0815*15) = 140e^(-1.2225) = 41.23°F