Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 16, Problem 8P
To determine
The reason that why the given situation is impossible.
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Why is the following situation impossible? A thin brass ring has an inner diameter 10.00 cm at 20.0°C. A solid aluminum cylinder has diameter 10.02 cm at 20.0°C. Assume the average coefficients of linear expansion of the two metals are constant. Both metals are cooled together to a temperature atwhich the ring can be slipped over the end of the cylinder.
A steel rod is 3.224 cm in diameter at 33.00°C. A brass ring has an interior diameter of 3.220 cm at 33.00°C. At what common
temperature will the ring just slide onto the rod? The linear expansion coefficient of steel is 11.00 x 106 1/C°. The linear expansion
coefficient of brass is 19.00 x 106 1/C°.
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A circular hole in an aluminum plate is 2.386 cm in diameter at 0.000°C. What is its diameter when the temperature of the plate is raised to 75.50°C? The
linear expansion coefficient of aluminum is 23.00 x 10-6 /C°.
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Chapter 16 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 16.2 - Consider the following pairs of materials. Which...Ch. 16.3 - Prob. 16.2QQCh. 16.4 - A common material for cushioning objects in...Ch. 16.4 - Prob. 16.4QQCh. 16.5 - Two containers hold an ideal gas at the same...Ch. 16.6 - Prob. 16.6QQCh. 16 - Prob. 1OQCh. 16 - A cylinder with a piston holds 0.50 m3 of oxygen...Ch. 16 - A hole is drilled in a metal plate. When the metal...Ch. 16 - When a certain gas under a pressure of 5.00 106...
Ch. 16 - Prob. 5OQCh. 16 - Prob. 6OQCh. 16 - What would happen if the glass of a thermometer...Ch. 16 - Prob. 8OQCh. 16 - A gas is at 200 K. If we wish to double the rms...Ch. 16 - Prob. 10OQCh. 16 - Prob. 11OQCh. 16 - A rubber balloon is filled with 1 L of air at 1...Ch. 16 - Prob. 13OQCh. 16 - An ideal gas is contained in a vessel at 300 K....Ch. 16 - Prob. 15OQCh. 16 - Prob. 16OQCh. 16 - Prob. 17OQCh. 16 - A sample of gas with a thermometer immersed in the...Ch. 16 - Prob. 19OQCh. 16 - Prob. 1CQCh. 16 - Prob. 2CQCh. 16 - Prob. 3CQCh. 16 - A piece of copper is dropped into a beaker of...Ch. 16 - Prob. 5CQCh. 16 - Prob. 6CQCh. 16 - Prob. 7CQCh. 16 - Prob. 8CQCh. 16 - Prob. 9CQCh. 16 - Prob. 10CQCh. 16 - Prob. 11CQCh. 16 - Prob. 12CQCh. 16 - Prob. 13CQCh. 16 - Prob. 1PCh. 16 - Convert the following to equivalent temperatures...Ch. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - A sample of a solid substance has a mass m and a...Ch. 16 - Each year thousands of children are badly burned...Ch. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - The active element of a certain laser is made of a...Ch. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - Prob. 18PCh. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - Prob. 21PCh. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - Prob. 25PCh. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - The mass of a hot-air balloon and its cargo (not...Ch. 16 - Prob. 30PCh. 16 - A popular brand of cola contains 6.50 g of carbon...Ch. 16 - Prob. 32PCh. 16 - At 25.0 m below the surface of the sea, where the...Ch. 16 - To measure how far below the ocean surface a bird...Ch. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - Prob. 38PCh. 16 - Prob. 39PCh. 16 - A cylinder contains a mixture of helium and argon...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - (a) How many atoms of helium gas fill a spherical...Ch. 16 - Fifteen identical particles have various speeds:...Ch. 16 - From the MaxwellBoltzmann speed distribution, show...Ch. 16 - Prob. 47PCh. 16 - Helium gas is in thermal equilibrium with liquid...Ch. 16 - Prob. 49PCh. 16 - Prob. 50PCh. 16 - Prob. 51PCh. 16 - Prob. 52PCh. 16 - A mercury thermometer is constructed as shown in...Ch. 16 - A liquid with a coefficient of volume expansion ...Ch. 16 - A clock with a brass pendulum has a period of...Ch. 16 - A vertical cylinder of cross-sectional area A is...Ch. 16 - Prob. 57PCh. 16 - Prob. 58PCh. 16 - Prob. 59PCh. 16 - The rectangular plate shown in Figure P16.60 has...Ch. 16 - In a chemical processing plant, a reaction chamber...Ch. 16 - Prob. 62PCh. 16 - Prob. 63PCh. 16 - Two concrete spans that form a bridge of length L...Ch. 16 - A 1.00-km steel railroad rail is fastened securely...Ch. 16 - Prob. 66PCh. 16 - Prob. 67PCh. 16 - Prob. 68PCh. 16 - Consider an object with any one of the shapes...Ch. 16 - Prob. 70PCh. 16 - Prob. 71PCh. 16 - Prob. 72PCh. 16 - Prob. 73PCh. 16 - A cylinder that has a 40.0-cm radius and is 50.0...Ch. 16 - Prob. 75P
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- 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?arrow_forwardTwo metal bars are made of invar and a third bar is made of aluminum. At 0C, each of the three bars is drilled with two holes 40.0 cm apart. Pins are put through the holes to assemble the bars into an equilateral triangle as in Figure P18.31. (a) First ignore the expansion of the invar. Find the angle between the invar bars as a function of Celsius temperature. (b) Is your answer accurate for negative as well as positive temperatures? (c) Is it accurate for 0C? (d) Solve the problem again, including the expansion of the invar. Aluminum melts at 660C and invar at 1 427C. Assume the tabulated expansion coefficients are constant. What are (e) the greatest and (f) the smallest attainable angles between the invar bars? Figure P18.31arrow_forwardA 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.arrow_forward
- 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)?arrow_forward(a) The inside of a hollow cylinder is maintained at a temperature Ta, and the outside is at a lower temperature, Tb (Fig. P19.45). The wall of the cylinder has a thermal conductivity k. Ignoring end effects, show that the rate of energy conduction from the inner surface to the outer surface in the radial direction is dQdt=2Lk[TaTbln(b/a)] Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2rL. (b) The passenger section of a jet airliner is in the shape of a cylindrical tube with a length of 35.0 m and an inner radius of 2.50 m. Its walls are lined with an insulating material 6.00 cm in thickness and having a thermal conductivity of 4.00 105 cal/s cm C. A heater must maintain the interior temperature at 25.0C while the outside temperature is 35.0C. What power must be supplied to the heater? Figure P19.45arrow_forwardThe measurement of the average coefficient of volume expansion for a liquid is complicated because the container also changes size with temperature. Figure P19.62 shows a simple means for measuring despite the expansion of the container. With this apparatus, one arm of a U-tube is maintained at 0C in a water-ice bath, and the other arm is maintained at a different temperature Tc in a constant-temperature bath. The connecting tube is horizontal. A difference in the length or diameter of the tube between the two arms of the U-tube has no effect on the pressure balance at the bottom of the tube because the pressure depends only on the depth of the liquid. Derive an expression for for the liquid in terms of h0, hi and Tc.arrow_forward
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- Question 2. Prayush is doing an experiment in thermodynamics with turpentine oil. He uses a 20.0 cm deep hollow cylinder made with aluminium. The cylinder has an internal capacity of 2.0 L and is completely filled with turpentine oil at 20.0° C. He then slowly heats the turpentine oil and the aluminum cylinder together to a temperature of 80.0° C. The coefficient of linear expansion of aluminium is 24 x 10-6(° C)-', volume expansion of turpentine is 9.0 x 10-4(°C)-!, and the specific heat capacity of aluminium is 900 J/kg°C respectively. (a) How much turpentine oil overflowsE (b) What is the volume of the turpentine remaining in the cylinder at 80.0°C? (c) How much heat must be added to the 30.0 kg aluminium cylinder in order to increase its internal capacity by 0.025 L ?arrow_forwardan aluminum rod is 10cm long and a steel rod is 80cm long when both rods are at 15 degrees C. Both rods have the same diameter. these rods are joined end to end to form a rod 90cm long. the coefficient of linear expansion of aluminum and steel are 2.4 x 10^-5 K^-1 and 1.2 x 10^-5 K^-1. the temperature is raised to 90 degreesC. the increase in the length of the joined rod, in mm, is closest to? - 0.9 -0.81 - 0.72 - 0.63 - 0.99arrow_forwardAn aluminum rod is 30.0 cm long and a steel rod is 90.0 cm long when both rods are at a temperature of 15°C. Both rods have the same diameter. The rods are joined end-to-end to form a rod 60.0 cm long. The coefficients of linear expansion of aluminum and steel are 24 x 10-5 K-1 and 1.2 x 10-5 K-1, respectively. The temperature is raised to 70° C. The increase in the length of the joined rod, in mm, is closest to:arrow_forward
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