### Thermal Expansion Concept**Problem Statement:**At 20.0 °C, an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm. Determine the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C.**Given:**- Coefficient of linear expansion for steel, \( \alpha_{\text{st}} = 11.0 \times 10^{-6} \, \text{C}^{-1} \)- Coefficient of linear expansion for aluminum, \( \alpha_{\text{al}} = 23.0 \times 10^{-6} \, \text{C}^{-1} \)**Diagrams:**1. **Diagram at 20.0 °C:** - A cross-sectional view showing the aluminum sleeve fitting exactly over the steel rod, both with diameters of 5.000 cm.2. **Diagram at 100.0 °C:** - A cross-sectional view showing a gap between the aluminum sleeve and the steel rod due to differential thermal expansion.**Explanation:**- As both materials are heated from 20.0 °C to 100.0 °C, they expand, but at different rates due to differing coefficients of thermal expansion.- The aluminum sleeve expands more than the steel rod, creating a gap.**Objective:**Calculate the size of the gap formed at 100.0 °C based on the thermal expansion properties of aluminum and steel.

Answered: Image /qna-images/answer/ec7ff19d-0688-46f7-be70-5c1f2cf704d3.jpg

TE-1 At 20.0 °C an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm as shown below. Find the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C. At 20.0°C At 100.0°C 11.0x10 23.0x10 steel Use a = and a %3D C° 5.000cm gap aluminum rch

TE-1 At 20.0 °C an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm as shown below. Find the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C. At 20.0°C At 100.0°C 11.0x10 23.0x10 steel Use a = and a %3D C° 5.000cm gap aluminum rch

Inquiry into Physics

8th Edition

ISBN:9781337515863

Author:Ostdiek

Publisher:Ostdiek

Chapter5: Temperature And Heat

Section: Chapter Questions

Problem 1MIO: In Section 5.2, we discussed the phenomenon of thermal expansion. Concept Map 5.4 was to have been...

See similar textbooks

Similar questions

One method at getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block he hotter or colder than the peg during insertion? Explain your answer.
Unreasonable Results (a) Calculate the rate of heat transfer by conduction through a window with an area of 1.00 m2 that is 0.750 cm thick, if its inner surface is at 22.00C and its outer surface is at 35.00C (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
Unreasonable Results (a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If 1he hole is 10.0% bigger in diameter than the 22.0C rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (2) Which premise is responsible?
The latent heat of vaporization for water at room temperature is 2 430 J/g. Consider one particular molecule at the surface of a glass of liquid water, moving upward with sufficiently high speed that it will be the next molecule to join the vapor. (a) Find its translational kinetic energy. (b) Find its speed. Now consider a thin gas made only of molecules like that one. (c) What is its temperature? (d) Why are you not burned by water evaporating from a vessel at room temperature?
In some countries, liquid nitrogen is used on dairy trucks instead of mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid nitrogen, which has a density at 808kg/m3. (a) Calculate the heat transfer necessary to evaporate this amount of liquid nitrogen and raise its temperature to 300C. (Use cp and assume it is constant over the temperature range.) This value is the amount of cooling the liquid nitrogen supplies. (b) What is this heat transfer rate in kilowatthours? (c) Compare the amount of cooling obtained from melting an identical mass at 0C ice with that from evaporating the liquid nitrogen.
You and your younger brother are designing an air rifle that will shoot a lead pellet with mass m = 1.10 g and cross-sectional area A = 0.030 0 cm3. The rifle works by allowing high-pressure air to expand, propelling the pellet down the rifle barrel. Because this process happens very quickly, no appreciable thermal conduction occurs and the expansion is essentially adiabatic. Your design is such that, once the pressure begins pushing on the pellet, it moves a distance of L = 50.0 cm before leaving the open end of the rifle at your desired speed of v = 120 m/s. Your design also includes a chamber of volume V = 12.0 cm3 in which the high-pressure air is stored until it is released. Your brother reminds you that you need to purchase a pump to pressurize the chamber. To determine what kind of pump to buy, you need to find what the pressure of the air must be in the chamber to achieve your desired muzzle speed. Ignore the effects of the air in front of the bullet and friction with the inside walls of the barrel.
Unreasonable Results Suppose the relative humidity is 80% on a day when the temperature is 30.0C. (a) What will the relative humidity be if the air cools to 25.0C and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible?
(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The walls' surface area is 120 m2 and their inside surface is at 18.0 , while their outside surface is at 5.00 . (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?
What does it mean to say that two systems are in thermal equilibrium?
The Surface temperature of the Sun is about 5750 K. What is this temperature on the Fahrenheit scale?
(a) The number of kilocalories in food is determined by calorimetry techniques in which the food is burned and the amount at heat transfer is measured. How many kilocalories per gram are there in a 5.00g peanut if the energy from burning it is transferred to 0.500 kg of water held in a 0.100kg aluminum cup, causing a 54.9C temperature increase? (b) Compare your answer to labeling information found on a package of peanuts and comment on whether the values are consistent.
An aluminum rod and an iron rod are joined end to end in good thermal contact. The two rods have equal lengths and radii. The free end of the aluminum rod is maintained at a temperature of 100.C, and the free end of the iron rod is maintained at 0C. (a) Determine the temperature of the interface between the two rods. (b) If each rod is 15 cm long and each has a cross-sectional area of 5.0 cm2, what quantity of energy is conducted across the combination in 30. min?