The copper rod is heated from
15°C to 95°C. What will its
increase in length be?
ǻL = LiĮǻT
ǻT = 95°C í 15°C = 80 C°
ǻL = (0.5 m)(1.65×10í^5 1/C°)(80 C°)
ǻL = 6.6×10í^4 m
18.9 - Sample problem: thermal expansion and stress
Above, you see an aluminum rod heated by the Sun and held in place with concrete blocks. Since the rod increases in temperature, its length
also increases. This exerts a force on the concrete blocks. Stress is force per unit area, and an equation for tensile stress was presented in
another chapter. Young’s modulus for aluminum is given; it relates the fractional increase in length (the strain) to stress. You are asked to find
the stress that results from the increase in temperature.
VariablesYou may notice that the initial length of the rod is not known. It is not needed to answer the question.
What is the strategy?- Combine the equations for thermal expansion and tensile stress to write an equation to calculate tensile stress from the temperature
change. - Use the equation to compute the stress in this case.
Physics principles and equationsWe will use the equations for thermal expansion and tensile stress. Tensile stress is measured as force per unit area, or F/A.
ǻL = LiĮǻT
F/A = Y(ǻL/Li)What stress does the aluminum rod
exert when its temperature rises
20 K?
thermal expansion coefficient Į = 2.31×10í (^5) 1/C°
Young’s modulus Y = 70×10^9 N/m^2
temperature change ǻT = 20 K
initial length Li
change in length ǻL
tensile stress F/A
(^340) Copyright 2007 Kinetic Books Co. Chapter 18