Chapter 8.2, Problem 3P

To determine

To calculate: Heat loss through a window with area $4.5{\text{ m}}^2$ when temperature difference is $12°\text{C}$ .

Answer to Problem 3P

Heat loss through a window with area $4.5{\text{ m}}^2$ when temperature difference is $12°\text{C}$ , is $\text{864 BTU}$ .

Explanation of Solution

Given information:

The following variation:

The heat loss through a glass window varies jointly as the area of the window and the difference between the inside and the outside temperatures.

When $\text{temperature difference = }15°\text{C}$ and ${\text{area = 3 m}}^2$ , $\text{heat loss =720 BTU}$ .

Calculation:

Let Q be the heat loss through the window, A be the area of the window and t be the temperature difference. Then, Q varies jointly as A and t that is,

  $Q=kAt$

where k is a constant.

Substituting $Q=720\text{ BTU}$ , $A{\text{ = 3 m}}^2$ and $t=15°\text{C}$ ,

  $\begin{array}{l}Q=kAt[\text{Equation]}\\ 720=k\left(3\right)\left(15\right)[\text{Substitute]}\\ 720=45k[\text{Multiply]}\\ k=\frac{720}{45}[\text{Divide both sides by 45]}\\ k=16[\text{Simplify]}\end{array}$

Therefore, an equation of the joint variation is $Q=16At$

To find Q when $A=4.5{\text{ m}}^2$ and $t=12°\text{C}$ , substitute in $Q=16At$ .

  $\begin{array}{l}Q=16At[\text{Equation]}\\ Q=\left(16\right)\left(4.5\right)\left(12\right)[\text{Substitute]}\\ Q=864[\text{Multiply]}\end{array}$