Problem 11E

According to Newton’s law of cooling, the temperature T of a body at time t is given by T = Ta+ (T0 – Ta) e-kt, where Ta is the ambient temperature, T0 is the initial temperature, and k is the cooling rate constant. For a certain type of beverage container, the value of k is known to be 0.025 min-1.

a. Assume that Ta = 36°F exactly and that T0 = 72.0 ± 0.5°F. Estimate the temperature T at time t = 10 min, and find the uncertainty in the estimate.

b. Assume that T0 = 72°F exactly and that Ta = 36.0 ± 0.5°F. Estimate the temperature T at time t = 10 min, and find the uncertainty, in the estimate.

Answer :

Step 1 of 3:

According to the Newton’s law of cooling, the temperature T of a body at time t is given by

Where, is the ambient temperature

is the initial temperature

k is the cooling rate constant.

Here the value of k is 0.025