1. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Lecture Notes

2. Where are these houses losing the most heat to the environment? Visible light Infrared light wavelength of ~10 μm Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

3. To maintain a building’s temperature, the power input to the building has to be equal to the power output to its surroundings. Power input - intentional heating (furnace), unintentional heating (electrical appliances, lights, people), and solar radiation. Power output - conduction and radiation to the outside world, and ventilation losses as warm air exits to the outside world. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

4. We will approach the physics through a set of experiments. The first explores how to model the cooling of thermal systems by plotting their energy loss against time. Under controlled experimental conditions the thermal time constant, a characteristic of thermal systems, can also be measured. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

5. Newton's Law of cooling - the rate of heat loss from an object is proportional to the difference in temperature between that object and its surroundings. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

6. Heat transfer occurs in three ways: conduction, convection, and radiation. Conduction - transfer of heat from high temperature to low temperature by the direct contact of atoms or molecules Convection - transfer of energy between a solid and a nearby gas or liquid in motion Radiation - transfer of heat through space (example: Sun heating Earth) Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

7. You can derive an expression for a thermal time constant if the process of heat transfer is limited to conduction (convection and radiation are negligible). Radiation, following Stefan-Boltzmann's Law (P=σAεT 4 ), can be minimized if the emissivity (ε) of the container is low Convection can be minimized by eliminating environmental factors such as air currents. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

8. Water is held in a thin-walled Styrofoam box The mass of water holds the heat and the Styrofoam transmits it in and out (k Styrofoam <<k water ). Box: thickness d, surface area A Water: mass m, specific heat capacity c. T = temperature of the water T o = temperature of the environment Note: the Styrofoam is thin enough that we don't have to consider its heat capacity. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

9. Rate of heat flow (measured in watts): If T < T o, heat flow is negative. If there is no phase change, ΔQ = mc ΔT Combining these to get how the temperature changes with time: Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

10. The rate of change of ΔT is proportional to the ΔT itself and is an exponential function. where ΔT 0 is the initial temperature difference τ is the thermal time constant In this case we find τ to be Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

11. If you plot the natural logarithm of ΔT you get a straight line whose slope is 1/ τ. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

12. An exponential decay with τ = 2 h. The time constant can be found by drawing a tangent line at t =0 and seeing where it crosses the x-axis. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

13. This method of finding the thermal time constant will only produce accurate results if the heat transfer mechanism is by conduction and if the outside temperature is constant. Experimentally this is difficult to achieve. See the take-home experiments for more information. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Home Heating

14. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia 1. David MacKay, Sustainable Energy, pp.140-154, 289- 306 www.withouthotair.comwww.withouthotair.com Home Heating