Thermodynamics and Atomic Physics II 1. Heat from a source at 550 K is added to the working fluid of an engine operating at a steady rate. The temperature of the surroundings is 300 K. The efficiency of this process is defined as the ratio of the mechanical power produced by the engine to the rate at which heat is provided. The maximum efficiency of this engine is: (a) much greater than 1. (b) about equal to 1. (c) much less than 1. (d) impossible to determine. 2. To determine the efficiency of a piston-and-cylinder based engine that uses air as a working fluid, the properties of which substances need to be known? (a) The air in the engine. (b) The metal of the engines pistons and cylinders. (c) The atmosphere surrounding the engine. (d) Both the engine air and the metal material. (e) All of the engine air, the engine metal, and the surrounding atmosphere. 3. An electric water heater consists of a perfectly-insulated tank filled with water and fitted with an electric heating element. Water enters the tank at 10 C and exits at 50 C at a pressure greater than 1 atm. The efficiency of the water heating process is defined as the energy provided to the water divided by the electrical energy provided to the heating element. The efficiency of the water heating process is: (a) much greater than 1. (b) about equal to 1. (c) much less than 1. (d) impossible to determine. For the next three questions: Air at high pressure and ambient temperature is contained in a perfectly insulated piston-cylinder device. Stops prevent the piston from moving up. The stops are then removed, and the piston quickly rises until a second set of stops (that prevents the piston from leaving the cylinder) is encountered. 4. The temperature of the air: (a) increases. (b) remains the same. (c) decreases. (d) cannot be determined. 5. The energy of the air in the cylinder: (a) increases. (b) remains the same. (c) decreases. (d) cannot be determined. 6. Work is done by the air in this process. (a) True. 1
(b) False. (c) Impossible to tell. 7. Three processes compose a thermodynamic cycle (see the pv diagram below). Process 1 2 takes place isothermally. Process 2 3 takes place isochorically, and process 3 1 is adiabatic. During the complete cycle, the total amount of work done is 10 J. During process 2 3, the internal energy decreases by 20 J; and during process 3 1, 20 J of work is done on the system. How much heat is added to the system during process 1 2? (b) 10 J (c) 20 J (d) 30 J (e) 40 J 8. The root mean square velocity of oxygen gas is v at room temperature. What is the root mean square velocity of hydrogen gas at the same temperature? (a) 16v (b) 4v (c) v (d) v/4 (e) v/16 9. A Carnot cycle takes in 1000 J of heat at a high temperature of 400 K. How much heat is expelled at the cooler temperature of 300 K? (b) 250 J (c) 500 J (d) 750 J (e) 1000 J 10. An ideal gas is expanded at constant pressure from an initial volume V i and an initial temperature T i to a final volume V f and final temperature T f. The gas has molar heat capacity C P at constant pressure. The amount of work done by n moles of the gas during the process can be expressed: (b) nrt i ln (V f /V i ) (c) C P n(t f T i ) (d) nk(v f V i ) (e) nr(t f T i ) 2
11. To raise the temperature of an ideal gas by 150 K, 6300 joules are required if the gas is heated isochorically, while 8800 joules are required if it is heated isobarically. How much does the internal energy of the gas change when its temperature is raised by 150 K? (a) 2500 J (b) 6300 J (c) 8800 J (d) 11,300 J (e) 15,100 J 12. Which of the following PV plots best represents an isothermal process? (a) (b) (c) (d) (e) 13. One end of a metal rod of length L and cross-sectional area A is held at constant temperature T 1. The other end is held at constant temperature T 2. Which of the following statements about the amount of heat transferred through the rod per unit time are true? I. The rate of heat transfer is proportional to 1/(T 1 T 2 ). II. The rate of heat transfer is proportional to A. III. The rate of heat transfer is proportional to L. (a) II only. (b) III only. (c) I and II only. (d) I and III only. (e) II and III only. 14. A mole of ideal gas at STP is heated in an insulated constant volume container until the average velocity of its molecules doubled. Its pressure would therefore increase by what factor?.5 3
(b) 1 (c) 2 (d) 4 (e) 8 15. The momentum p of a photon is given by the equation p = h λ where h is Plancks constant and λ is the photons wavelength. In terms of p, the photon s energy is (a) E γ = phc (b) E γ = ph/c (c) E γ = p/c (d) E γ = pc (e) E γ = h/pc 16. The photoelectric work function of a metal surface is Φ. The thermionic work function of the same metal surface will be (a) less than Φ. (b) equal to Φ. (c) greater than Φ. (d) independent of Φ. (e) dependent on the heating method. 17. In an experiment, light of a particular wavelength is incident on a metal surface, and electrons are emitted from the surface as a result. To produce more electrons per unit time but with less kinetic energy per electron, the experimenter should do which of the following? (a) Increase the intensity and decrease the wavelength of the light. (b) Increase the intensity and the wavelength of the light. (c) Decrease the intensity and the wavelength of the light. (d) Decrease the intensity and increase the wavelength of the light. (e) None of the above would produce the desired result. 18. The classical planetary model of the hydrogen atom is unacceptable because (a) the Coulomb force is too week to hold the electron. (b) the nuclear force is too strong to allow the electrons to orbit. (c) the electron is accelerating and must radiate away its energy. (d) the electron s angular momentum is not conserved, as it should be. (e) of some other reason. 19. When a photon is Compton-scattered, the (a) minimum shift λ will be twice the Compton wavelength. (b) minimum shift λ will be h times the Compton wavelength. (c) maximum shift λ will be h times the Compton wavelength. (d) maximum shift λ will be twice the Compton wavelength. 4
(e) shift λ will be impossible to predict. 20. The energy per unit area per unit time radiate by a blackbody (a) depends on the mass of the blackbody. (b) depends on the color of the blackbody. (c) depends on its temperature. (d) depends on its total surface area. (e) depends on something other than the things mentioned. 5