(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount Δ L when its temperature changes by Δ T , the stress is equal to F A = Y ( Δ L L 0 − α Δ T ) where F is the tension on the rod, L 0 is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends ( Fig. P17.79 ). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but state them. Figure P17.79
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount Δ L when its temperature changes by Δ T , the stress is equal to F A = Y ( Δ L L 0 − α Δ T ) where F is the tension on the rod, L 0 is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends ( Fig. P17.79 ). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but state them. Figure P17.79
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount ΔL when its temperature changes by ΔT, the stress is equal to
F
A
=
Y
(
Δ
L
L
0
−
α
Δ
T
)
where F is the tension on the rod, L0 is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends (Fig. P17.79). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but state them.
Consider liquid water at 1 atm. At 25◦C, the density of water is 0.997044 g cm−3 . The coefficient of thermal expansion, α, is well fitted by α = e + ft + gt2 where t is in celsius and e = −1.00871 × 10-5 K−1 , f = 1.20561 × 10-5 C −1 K−1 , and g = −5.4150 ×10-8 C−2 K−1 . What is the density of the water at 38◦C
A thermal window, with an area of 6.0m ^ 2, is constructed of two layers of glass, each 4.0mm thick, separated from each other by a 5.0mm air gap. If the inner surface is at 20.0 ° C and the outer surface is at -5.0 ° C, what is the rate of energy transfer by conduction through the window? The thermal conductivity of glass is 0.8 W⁄ (m. ° C) and that of air is 0.023 W⁄ (m. ° C)
A solid aluminum alloy [E=69 GPa; α=23.6×10−6/C∘] rod (1) is attached rigidly to a solid brass [E=115 GPa; α=18.7×10−6/C∘] rod (2), as shown in the figure. The compound rod is subjected to a tensile load of P=5.3 kN. The diameter of each rod is 11 mm. The rods lengths are L1=507 mm and L2=705 mm. Compute the change in temperature required to produce zero horizontal deflection at end C of the compound rod.
Chapter 17 Solutions
University Physics with Modern Physics (14th Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
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