**27. ssm A steel ruler is calibrated to read true at 20.0 °C. A draftsman uses the ruler at 40.0 °C to draw a line on a 40.0 °C copper plate. As indicated on the warm ruler, the length of the line is 0.50 m. To what temperature should the plate be cooled, such that the length of the line truly becomes 0.50 m?

**27. ssm A steel ruler is calibrated to read true at 20.0 °C. A draftsman uses the ruler at 40.0 °C to draw a line on a 40.0 °C copper plate. As indicated on the warm ruler, the length of the line is 0.50 m. To what temperature should the plate be cooled, such that the length of the line truly becomes 0.50 m?

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Temperature

Section: Chapter Questions

Problem 45CP: A 1.00-km steel railroad rail is fastened securely at both ends when the temperature is 20.0C. As...

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The average coefficient of linear expansion of copper is 17 106 (C)1. The Statue of Liberty is 93 in tall on a summer morning when the temperature is 25C. Assume the copper plates covering the statue are mounted edge to edge without expansion joints and do not buckle or bind on the framework supporting them as the day grows hot. What is the order of magnitude of the statues increase in height? (a) 0.1 mm (b) 1 mm (c) 1 cm (d) 10 cm (e) 1 m
Inside the wall of a house, an L-shaped section of hot-water pipe consists of three parts: a straight horizontal piece h = 28.0 cm long, an elbow, and a straight, vertical piece = 134 cm long (Fig. P10.51). A stud and a second- story floorboard hold the ends of this section of copper pipe stationary. Find the magnitude and direction of the displacement of the pipe elbow when the water flow is turned on, raising the temperature of the pipe from 18.0C to 46.5C. Figure P10.51
A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P20.55). One end of the compound bar is maintained at 80.0C, and the opposite end is at 30.0C. When the energy transfer reaches steady state, what is the temperature at the junction?
Two concrete spans that form a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P16.63a). If a temperature increase of T occurs, what is the height y to which the spans rise when they buckle (Fig. P16.63b)?
The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is 35.0 . What will its height be on a day when the temperature falls to -10.0 ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.
A spherical shell has inner radius 3.00 cm and outer radius 7.00 cm. It is made of material with thermal conductivity k = 0.800 W/m C. The interior is maintained at temperature 5C and the exterior at 40C. After an interval of time, the shell reaches a steady state with the temperature at each point within it remaining constant in time. (a) Explain why the rate of energy transfer P must be the same through each spherical surface, of radius r, within the shell and must satisfy dTdr=P4kr2 (b) Next, prove that 5dT=P4k0.030.07r2dr where T is in degrees Celsius and r is in meters. (c) Find the rate of energy transfer through the shell. (d) Prove that 5TdT=1.840.03rr2dr where T is in degrees Celsius and r is in meters. (e) Find the temperature within the shell as a function of radius. (f) Find the temperature at r = 5.00 cm, halfway through the shell.
A 1.00-km steel railroad rail is fastened securely at both ends when the temperature is 20.0C. As the temperature increases, the rail buckles, taking the shape of an arc of a vertical circle. Find the height h of the center of the rail when the temperature is 25.0C. (You will need to solve a transcendental equation.)
The rectangular plate shown in Figure P16.60 has an area Ai equal to w. If the temperature increases by T, each dimension increases according to Equation 16.4, where is the average coefficient of linear expansion. (a) Show that the increase in area is A = 2Ai T. (b) What approximation does this expression assume?