Phys11 - Unit 11 Thermal Behavior of Matter and Heat...

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1 Unit 11 Thermal Behavior of Matter and Heat Engines 11.1 Thermal expansion 11.2 Heat and mechanical work 11.3 Heat capacity 11.4 Specific heat 11.5 Latent Heat 11.6 Conduction 11.7 Convection 11.8 Radiation 11.9 Heat engines and the Carnot cycle 11.1 Thermal expansion Most substances expand when heated. The expansion of liquid, such as mercury or alcohol, results in a column of liquid of variable height within the glass neck of the thermometer. 11.11 Linear expansion The change in the length of rod is directly proportional to the change in temperature. The constant of proportionality is referred to as α and L 0 is the initial length of the rod. T L L = 0 SI unit for : K 1 = ( C o ) 1 . Alternatively, we can refer as the fractional change of length per unit change of temperature, e.g. 0 1 L LT ⎛⎞ = ⎜⎟ ⎝⎠ .
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2 Substance Coefficient of Expansion, α (K 1 ) Lead 29 × 10 6 Aluminum 24 × 10 6 Copper 17 × 10 6 Iron (Steel) 12 × 10 6 Concrete 12 × 10 6 Window glass 11 × 10 6 Quartz 0.50 × 10 6 Table: Coefficients of thermal expansion An interesting application of thermal expansion is in the behavior of a bimetallic strip. As the name suggests, a bimetallic strip consists of two metals bonded together to form a linear strip of metal. Since two different metals will, in general, have different coefficients of linear expansion, , the two sides of the strip will change lengths by different amounts when heated or cooled. Refer to the figure. (a) A bimetallic strip composed of metals A and B . If metal B has a larger coefficient of linear expansion than metal A , it will shrink more when cooled (b), and expand more when heated (c). A bimetallic strip can be used to construct a thermostat (d). If the temperature falls, the strip bends downward and closes the electrical circuit, which then operates a heater. When the temperature rises, the strip deflects in the opposite direction, breaking the circuit and turning off the heater. Thermal expansion, though small, is far from negligible in many everyday situations. This is especially true when long objects such as railroad tracks, bridges, or pipelines are involved. Bridges and elevated highways, must include expansion joints to prevent the roadway from buckling when it expands in hot weather. Similarly,
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3 pipelines typically include loops that allow for expansion and contraction when the temperature changes. 11.12 Area expansion Since the length of an object changes with temperature, it follows that its area changes as well. The initial area of the square is A = L 2 . If the temperature of the square is changed by T , and the length of each side of the square by L , ) 2 ( ) ( ) ( ' 2 2 2 2 2 2 2 T L T L L T L L L L A + + = + = + = α . Neglect the higher order term, e.g. 2 2 2 T L , since 2 2 T relatively small, we have T A A T L L A + = + = 2 2 ' 2 2 That is T A A 2 .
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This note was uploaded on 09/06/2010 for the course BSC PHY1417 taught by Professor Prof during the Spring '08 term at HKU.

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Phys11 - Unit 11 Thermal Behavior of Matter and Heat...

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