This constant k is the thermal conductivity . L T T A k t Q 2 1 − = Δ Δ T 1 T 2 26 i>Clicker Question • Assuming that no heat is lost through the side walls and that the hot and cold ends both maintain their temperature, the heat flowing through the two cross sectional surfaces is 1. Larger through A1 2. Larger through A2 3. Same through both areas. A1 A2 27 Thermal Energy and Power; Transforming Energy; Energy in Humans; Temperature; Heat; Conduction ; Home Heating • Metals are good thermal conductors: cooling of transistors, heat exchangers, cooking pots. • Materials commonly used for retaining heat have small thermal conductivity: wool sweaters, fiberglass insulation, air (thermos, thermal windows). (Generally porous materials or materials with little density.) • Double paned windows reduce heat conduction due to an air gap between the two glass panels. What would insulate better than air?
10 28 Thermal Conductivity Table 0.024 Polyurethane 0.023 Air 0.048 Fiberglass 0.1 Wood 0.84 Concrete 0.84 Brick 0.84 Glass 40 Steel 380 Copper 420 Silver k W/(m K) Material 29 • If you wanted to decrease the heat loss through a window on cold days, what could you do? A. Increase the thickness of the glass. B. Use a glass with a smaller k-value. C. Use a smaller size window. D. Decrease the temperature inside. E. All of the above. L T T A k t Q 2 1 − = Δ Δ i>Clicker Question 30 Thermal Energy and Power; Transforming Energy; Energy in Humans; Temperature; Heat; Conduction; Home Heating • The heat conduction equation can be used when calculating heat loss from homes: • Inside and outside temperatures remain constant over relatively long periods of time (hours). Over the course of a day, month, or year, we can use average temperatures. • The area through does not change. • Main heat loss channels are known: Walls, windows, doors, roof.
11 31 Thermal Energy and Power; Transforming Energy; Energy in Humans; Temperature; Heat; Conduction; Home Heating • Constant temperature inside: Dynamic equilibrium . • Conservation of energy: Energy flow into house + energy generated inside = energy flow out. House Energy generated inside house Energy Flow Out (heat loss to cold air) Energy Flow In (from sunshine) Energy Flow In (“fuel”) 32 • A little wooden cabin with 15 cm thick walls is equipped with a 1000 W space heater. The temperature outside drops to 5 ºC at night. The cabin is 10 m long and 10 m wide and 3 m high. The floor and the roof are insulated, while the walls have no insulation. What is the temperature inside? Example 33 Step 1: Interpret the Problem Carefully read and visualize the events described in the problem If necessary, sketch a picture to clarify sizes, directions and spatial relationships
12 34 Step 2: Identify the Relevant Physics Concepts • The cabin is in dynamic equilibrium. So the temperature inside and the temperature outside are constant.
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