Chapter 8.1, Problem 12P

To determine

To find the rate of cooling when the temperature is $\text{100°C}$ .

Answer to Problem 12P

The rate of cooling is $\text{16°C}$ per minute.

Explanation of Solution

Given information:

The given statement is:

“Newton’s Law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At the moment a steel plate at $\text{270°C}$ is placed in air that is at $\text{20°C}$ , its rate of cooling is $\text{50°C}$ per minute. How fast is it cooling when the temperature is $\text{100°C}$ ?”

Calculation :

The speed can be calculated by:

  $\begin{array}{l}\frac{y_1}{x_1-20}=\frac{y_2}{x_2-20}\\ \frac{50}{270-20}=\frac{y_2}{100-20}\\ y_2=\frac{50\times 80}{250}\\ y_2=16\end{array}$

Hence, the rate of cooling is $\text{16°C}$ per minute.