Chapter 0.1, Problem 42E

(a)

To determine

To find: Find the change in temperature of gypsum wallboard.

Answer to Problem 42E

Temperature is decreasing ${10}^0$ per inch.

Explanation of Solution

Given information:

Given figure is below:

  

Concept used: Formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

The gypsum board insulation is represented by the area color in grey.

Let’s take two point of this area from the graph.

Point $\left(0,72\right)$ and $\left(0.2,70\right)$ .

Apply the formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$ .

Substitute $x_1=0,y_1=72,x_2=0.2,y_2=70$

  $\begin{array}{l}m=\frac{70-72}{0.2-0}\\ m=\frac{-2}{0.2}\\ m=-10\end{array}$

Temperature is changing ${10}^0$ per inch. Negative sign indicates the decrease in temperature.

(b)

To determine

To find: Find the change in temperature of fiberglass.

Answer to Problem 42E

Temperature is decreasing ${16}^0$ per inches.

Explanation of Solution

Given information:

Given figure is below:

  

Concept used: Formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

The fiberglass board is represented by the area color in brown.

Let’s take two point of this area from the graph.

Point $\left(1,58\right)$ and $\left(4,10\right)$ .

Apply the formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$ .

Substitute $x_1=1,y_1=58,x_2=4,y_2=10$

  $\begin{array}{l}m=\frac{10-58}{4-1}\\ m=\frac{-48}{3}\\ m=-16\end{array}$

Temperature is changing ${16}^0$ inches. Negative sign indicates the decrease in temperature.

(c)

To determine

To find: Find the change in temperature of wood sheathing.

Answer to Problem 42E

Temperature is decreasing ${20}^0$ per inches.

Explanation of Solution

Given information:

Given figure is below:

  

Concept used: Formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

The gypsum board is represented by the area in checks.

Let’s take two point of this area from the graph.

Point $\left(4.2,8\right)$ and $\left(4.8,6\right)$ .

Apply the formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$ .

Substitute $x_1=4.2,y_1=8,x_2=4.8,y_2=4$

  $\begin{array}{l}m=\frac{4-8}{4-4.2}\\ m=\frac{-4}{-0.2}\\ m=-20\end{array}$

Temperature is changing ${20}^0$ per inches. Negative sign indicates the decrease in temperature.

(d)

To determine

To find: Find which of three materials is best insulator and which is poor.

Answer to Problem 42E

The best insulating material is gypsum wallboard and poor insulator is wood sheathing.

Explanation of Solution

Given information:

Temperature is decreasing , ${20}^0$ per inches for wood sheathing, ${16}^0$ per inches for fiber glass, ${10}^0$ per inch is for gypsum wallboard.

The best insulator is Gypsum wallboard because the temperature decrease is least by Gypsum wallboard.

Since the temperature is decreased highest by wood sheathing hence it is poor insulator.