Problem 28E

Refer to Exercise 16. Assume that T0 = 73.1 ± 0.1 °F, Ta = 37.5 ± 0.2°F, k = 0.032 min-1 with negligible uncertainty, and T = 50°F exactly. Estimate t, and find the relative uncertainty in the estimate.

Exercise 16: According to Newton’s law of cooling, the time t needed for an object at an initial temperature T0 to cool to a temperature T in an environment with ambient temperature Ta is given by

where k is a constant. Assume that for a certain type of container, k = 0.025 min-1. Let t be the number of minutes needed to cool the container to a temperature of 50oF. Assume that and . Estimate t, and find the uncertainty in the estimate.

Solution

Step 1 of 4

Here we have to find the uncertainty of time t needed for an object

according to newton’s law of cooling

Given initial temperature

From this T0=73.1,

Given cool to a temperature

Given ambient temperature

From this Ta=37.5,

And k=0.032 min-1