lecturenotes-April14

lecturenotes-April14 - 19%As 21%Bs 30%Cs 16%Ds 6Ds 11Cs 8Bs...

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19% As 21% Bs 30% Cs 16% Ds 7 As 8 Bs 11 Cs 6 Ds New Distribution
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18‐6 Thermal Expansion: Area Expansion in 1-D Δ L = α L 0 Δ T L = L 0 1 + αΔ T ( ) A = L 0 1 + Δ T ( ) W 0 1 + Δ T ( ) Expansion in 2-D Δ A = A 0 1 + Δ T ( ) 2 A 0 = A 0 2 Δ T + Δ T ( ) 2 ( ) A 0 2 ( ) Δ T A 0 β Δ T = 2
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18‐6 Thermal Expansion of Holes Do holes expand or contract when heated? Does radius increase or decrease when heated? The hole gets larger too!
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When the temperature of the piece of metal shown below is increased and the metal expands, what happens to the gap between the ends? 1. It becomes narrower 2. It becomes wider 3. It remains unchanged Question
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Checkpoint #2 : the fgure here shows Four rectangular metal plates, with sides oF L, 2L, or 3L. The expansion coefficient is the same. Rank the plates according to the expected increase in (a) their ver±cal heights and (b) their areas, greatest frst.
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18‐6 Volume Expansion Expansion in 1-D Δ L = α L 0 Δ T L = L 0 1 + αΔ T ( ) width height Expansion in 3-D V = L 0 1 + T ( ) [ ] W 0 1 + T ( ) [ ] H 0 1 + T ( ) [ ] Volume expansion coefFcients solids : 1 87 × 10 6 C liquids : 210 1100 × 10 6 C gasses : 3400 × 10 6 C Expansion in 2-D Δ A A 0 2 ( ) Δ T A 0 β A Δ T Δ V = V 0 1 + T ( ) 3 V 0 = V 0 3 T + 3 T ( ) 2 + T ( ) 3 ( ) V 0 3 ( ) Δ T V 0 V Δ T β V = 3 α --- coefFcient of volume expansion
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Steel α =11x10 6 / C o Δ V s = V 0 3 s ( ) gasoline = 950x10 6 / C o Δ V g = V 0 3 g ( ) Δ V = V s ( T ) V g ( T ) = V 0 (3 s 3 g ) Δ t Δ V = 70 x 3 x 2.817 x 10 6 x 20 = 1.18 x 10 2 ? L Check my numbers. Problem : Gas tank in the sun The 70-L steel gas tank of a car is Flled to the top with gasoline at 20 ° C. The car is then left to sit in the sun, and the tank reaches a temperature of 40 ° C. How much gasoline do you expect to over±ow from the tank? [gasoline has a coefFcient of volume expansion of 950 × 10 -6 / ° C ] 18‐6 Volume Expansion
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18‐7: Temperature and Heat If two objects are NOT in thermal equilibrium, their temperatures must be different. To make their temperatures equal (i.e. thermal equilibrium), HEAT MUST FLOW. HEAT has to do with the transfer of thermal energy. Symbol for HEAT: Q - BE VERY CAREFUL ABOUT THE SIGN “System”- particular objector or set of objects “Environment” - everything else in the universe Heat is negative when energy is transferred from the system’s thermal energy to its environment (heat is released or lost) Heat is zero when no energy is transferred between the system’s thermal energy and its environment (AT THERMAL EQUILIB) Heat is positive when energy is transferred to the system’s thermal energy from its environment (heat is absorbed)
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18‐7: Heat: transfer of thermal energy Remember: WORK (W) - energy transferred to system via a force acting on it calorie : “the amount of heat that would raise the temperature of 1 g of water from 14.5 ° C to 15.5 ° C Units : Btu : “the amount of heat that would raise the temperature of 1 lb of water from 63 ° F to 64 ° F Mechanical equivalent to Heat : 1 cal =3.969 × 10 -3 Btu = 4.1860 J James Joule (1818-1889) -> A given amount of work done is equivalent to a particular amount of heat input Joule : “ the amount of work done when a force of one Newton acts through a distance of one meter”
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lecturenotes-April14 - 19%As 21%Bs 30%Cs 16%Ds 6Ds 11Cs 8Bs...

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