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One-mole of a monatomic ideal gas goes through a quasistatic three
PRACTICE MIDTERM 1 Physics 306 5 March 2009 Please note: The first page of the actual in-class exam will look like this page. Any information you’d like other than the numerical constants listed here should be on your 3”x5” note card. NAME: _________________________________________ This exam is closed book. You are allowed a notecard with information of your own choosing. The exam is 1 hours in length. Graded exams will be returned in class on Tuesday, 10 March. Some numerical constants: kB=Boltzmann’s constant =1.38x10 -23 J/K NA=Avogadro’s number = 6.02x10 23 R=gas constant = 8.315 J/mol-K 1 atm=1.013x105 N/m2 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 _________ _________ _________ _________ _________ Total __________ Problem 1 You are given an Einstein solid with three oscillators and as well a two-state paramagnet with four spins. The magnetic field in the region of the paramagnet points “up” and is carefully tuned so that µB = , where µB is the energy of a spin antiparallel to B, and -µB is the energy of a spin parallel to B, while is the energy level separation of the oscillators. Initially, the two systems are separated and the energy in the Einstein solid U S is 4 and the energy in the paramagnet U P is -4 . (a) Using a schematic drawing of the Einstein solid, give an example of a microstate which corresponds to the macrostate U S = 4 . (b) Using a schematic drawing of the paramagnet, give an example of a microstate which corresponds to the macrostate U P = -4 . (c) Considering that the “system” comprises the solid and the paramagnet, calculate the multiplicity of the system assuming that the solid and paramagnet cannot exchange energy. Now let the solid and paramagnet exchange energy until they come to thermal equilibrium. (d) What is the value of US now? Draw an example of a microstate in which you might find the solid. (e) What is the value of UP now? Draw an example of a microstate in which you might find the paramagnet. V T 1 21 32 Problem 2 A system is comprised of 0.25 mole of an ideal monatomic gas at 0 0C and P=1 bar. When 3400 J of thermal energy are added to the system at constant pressure, the resultant expansion causes the system to perform 900 J of work. (a) Calculate the initial state (P,V,T) (b) Calculate the final state (P,V,T) (c) Calculate the change in internal energy for the process, U (d) Calculate the change in entropy for the process, S. Problem 3 One mole of an ideal diatomic gas goes through a quasi-static three-stage cycle (1-2, 2-3, 3-1) shown in the figure. Process 3-1 is adiabatic; V1 and V2 are given. P 1 3 2 V1 V2 V Calculate the entropy change for each stage and for the whole cycle, Stotal (express all the results in terms of given V1 and V2). Problem 4 A 0.5 kg piece of metal at 800C is dropped into a large pool of water at 200C. The metal has a specific heat at constant pressure of 100 J/(kgK) independent of temperature. How much does the entropy of the metal change? How much does the total entropy (of both the metal and water) change? Does it increase or decrease? Problem 5 Imagine that we rapidly compress a sample of air whose initial pressure is 105 Pa and temperature is 220C to a volume that is a quarter of its original volume. What is the final temperature of the air?
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