Chapter 1.7, Problem 57P

Home owners and builders discuss thermal conductivities in terms of the R value (R for resistance) of a material, defined as the thickness divided by the thermal conductivity: $R\equiv \frac{\Delta x}{k_t}.$

1. Calculate the R value of a 1/8-inch (3.2 mm) piece of plate glass, and then of a 1 mm layer of still air. Express both answers in SI units.
2. In the United States, R values of building materials are normally given in English units, °F·ft²Â·hr/Btu. A Btu, or British thermal unit, is the energy needed to raise the temperature of pound of water by 1°F. Work out the conversion factor between the SI and English units for R values. Convert your answers from part (a) to English units.
3. Prove that for a compound layer of two different materials sandwiched together (such as air and glass, or brick and wood), the effective total R value is the sum of the individual R values.
4. Calculate the effective R value of a single piece of plate glass with a 1.0-mm layer of still air on each side. (The effective thickness of the air layer will depend on how much wind is blowing; 1 mm is of the right order of magnitude under most conditions.) Using this effective R value, make a revised estimate of the heat loss through a 1-m² single-pane window when the temperature in the room is 20°C higher than the outdoor temperature.