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.

Refer to 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 T_a?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 50?F. Assume that T₀ = 70.1 ? 0.2?F and T_a = 35.7 ? 0.1?F. Estimate t, and find the uncertainty in the estimate.

In(To Ta) In(T Ta) | t = k k