qr code scanner java download Figure 13-20 The extreme temperatures of a summer day caused these railroad tracks to buckle in Objective-C

Generate Quick Response Code in Objective-C Figure 13-20 The extreme temperatures of a summer day caused these railroad tracks to buckle

Figure 13-20 The extreme temperatures of a summer day caused these railroad tracks to buckle
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Thermal Expansion of Solids
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It is standard practice for engineers to design small gaps, called expansion joints, into concrete-and-steel highway bridges to allow for the expansion of parts in the heat of summer Objects expand only a small amount when they are heated, but that small amount could be several centimeters in a 100-m-long bridge If expansion gaps were not present, the bridge could buckle or parts of it could break High temperatures can also damage railroad tracks that are laid without expansion joints, as shown in Figure 13-20 Some materials, such as the ovenproof glass that is used for cooking and laboratory experiments, are designed to have the least possible thermal expansion Large telescope mirrors are made of a ceramic material that is designed to undergo essentially no thermal expansion To understand the expansion of heated solids, picture a solid as a collection of particles connected by springs that represent the attractive forces between the particles When the particles get too close, the springs push them apart When a solid is heated, the kinetic energy of the particles increases, and they vibrate rapidly and move farther apart, weakening the
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(t)file photo, (b)courtesy US Department of Transportation
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attractive forces between the particles As a result, when the particles vibrate more violently with increased temperature, their average separation increases and the solid expands The change in length of a solid is proportional to the change in temperature, as shown in Figure 13-21 A solid will expand in length twice as much when its temperature is increased by 20 C than when it is increased by 10 C The expansion also is proportional to its length A 2-m bar will expand twice as much as a 1-m bar with the same change in temperature The length, L2, of a solid at temperature T2 can be found with the following equation, where L1 is the length at temperature T1 and alpha, , is the coefficient of linear expansion L2 L2 L1 L1 L Coefficient of Linear Expansion L1(T2 L1(T2 L1 T
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Lower temperature
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Figure 13-21 The change in length of a material is proportional to the original length and the change in temperature
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T1) T1)
Using simple algebra, you can solve for
The coefficient of linear expansion is equal to the change in length, divided by the original length and the change in temperature
The unit for the coefficient of linear expansion is 1/ C, or ( C) 1 Since solids expand in three directions, the coefficient of volume expansion, , is about three times the coefficient of linear expansion
V V1 T The coefficient of volume expansion is equal to the change in volume divided by the original volume and the change in temperature
Coefficient of Volume Expansion
Again, the unit for is 1/ C, or ( C) 1 The two coefficients of thermal expansion for a variety of materials are given in Table 13-2
Table 13-2
Coefficients of Thermal Expansion at 20 C Material Solids Aluminum Glass (soft) Glass (ovenproof) Concrete Copper Liquids Methanol Gasoline Water Coefficient of Linear Expansion, ( C) 1 25 9 3 12 16 10 10 10 10 10
6 6 6 6 6
Coefficient of Volume Expansion, ( C) 1 75 27 9 36 48 10 10 10 10 10
6 6 6 6 6
1200 10 950 10 210 10
6 6 6
Section 134 Solids
Linear Expansion A metal bar is 160 m long at room temperature, 21 C The bar is put into an oven and heated to a temperature of 84 C It is then measured and found to be 17 mm longer What is the coefficient of linear expansion of this material
Analyze and Sketch the Problem
Sketch the bar, which is 17 mm longer at 84 C than at 21 C Identify the initial length of the bar, L1, and the change in length, L Known:
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