Conceptual Physics

The insulating effectiveness of building materials is usually specified by an R-value. A

material with a high R-value is a good insulator. For a slab of material of a given

thickness, the thermal resistanceR is defined, as you see in Equation 3, as the

thickness of the slab divided by its thermal conductivity. This is often called the R-value

in the building trade. The SI units for R are square meters·kelvin per watt, and the

building material ratings are then often called RSI-values. We show metric values with

that name in the table above.

In North America, R-values based on the British measurement system are commonly

used for building materials. These R-values have units of square feet·Fahrenheit

degrees·hours per British thermal unit. We list them also in the table above. The

thickness of the material for both RSI- and R-values is one inch, which is typical for

building materials.

The term k in the equation in Equation 2 can be replaced with an expression involving

R. This yields another equation, also shown in Equation 3, for the rate of heat transfer.

Considering these equations and studying the table above can help you understand

why certain materials are chosen in construction. First, increasing the thickness of a

material increases its R-value, so you see thicker insulating material in a colder

environment where the temperature difference between inside and outside is greater.

Second, some materials have high k (low R) values, making them unlikely choices for

insulators. For instance, building a house out of copper would lead to high heating costs

(not to mention building costs). Building materials such as polyurethane foam are

effective insulators and can be combined with other reasonably good insulators such as

wood for even greater energy efficiency.

Third, materials can be combined. Double-paned windows trap a quantity of an inert

gas like argon between two layers of glass. Argon has a high R value and considerably

reduces the rate of heat transfer through the window.

Heat conduction

Rate of heat transfer depends on:

·thermal conductivity

·area

·temperature difference

·thickness

Rate of heat transfer, definition

Pc = Q/t

Pc = rate of heat transfer (J/s)

Q = heat transferred

t = time

Rate of heat transfer, calculated

k = thermal conductivity

A = area

ǻT = temperature difference

L = thickness

k units: J/s·m·K = W/m·K

Thermal resistance

R = L/k

R = thermal resistance

R units (SI): m^2 ·K/W

R units (British): ft^2 ·F°·h/Btu

(^350) Copyright 2007 Kinetic Books Co. Chapter 18