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Chapter 16: Problem 32

Find the \(\mathcal{R}\) -factor for a wall that loses 0.040 Btu each hour through each square foot for each \(^{\circ} \mathrm{F}\) temperature difference.

Short Answer

Expert verified
The \(\mathcal{R}\) -factor of the wall is \(1/0.040 = 25 \, hr \cdot ft^2 \cdot °F/Btu\).

Step by step solution

01

Understand Concept of \(\mathcal{R}\) -factor

The \(\mathcal{R}\) -factor is the measure of thermal resistance, which is the ability of a material or assembly to resist the flow of heat. It utilizes the units \(hr \cdot ft^2 \cdot °F/Btu\). The value of the \(\mathcal{R}\) -factor indicates how well the material insulates. Higher numbers mean better insulation.
02

Apply Given Data

We have the rate of heat loss given as 0.040 \(Btu/hr/ft^2/°F\). This is actually the inverse of the \(\mathcal{R}\) -factor as per the unit's consideration. The \(\mathcal{R}\) -factor is exactly opposite, it is the amount of resistance to the heat flow.
03

Calculate \(\mathcal{R}\) -factor

As explained in Step 2, that the given heat loss measurement is inverse of \(\mathcal{R}\) -factor, we simply find the reciprocal of it. Thus, the \(\mathcal{R}\) -factor will be \(1 / 0.040 Btu/hr/ft^2/°F\) for the wall.

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