# FinalExam-practice-2010s-answers - PHYS 172 Spring 2010...

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1 PHYS 172 Spring 2010 Final exam practice (With answers) 1. The final exam will have 20 multiple choice questions and therefore cannot and does not cover everything that was presented in the course. While the practice exam difficulty level is similar to the real final exam, the material covered in each of the exams does not necessarily coincide. For example, there is no problem on collision in practice exam, but such a problem may appear in final exam since respective material was covered in the lectures. 2. You are expected to make your own equation sheet: two sided letter size page is the limit. There is no limit on what and how you write on that page.

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2 Problem 1. A penny that is initially at room temperature (20 C) is dropped into a thermos with coffee that is initially heated to 90 C. Assuming that coffee and the penny in thermos form a closed system, what happens with the entropy in the process of equilibration? A) The total entropy of the system increases B) The total entropy of the system decreases C) The entropy of a penny increases, entropy of coffee decreases, and the total entropy of the system stays constant. D) The entropy of a penny decreases, entropy of coffee increases, and the total entropy of the system stays constant. E) The entropies of both penny and coffee increases, and so does the total entropy. Problem 2 Consider a system of 8 one-dimensional harmonic oscillators. Initially this system has 3 quanta of energy. By how much does the entropy change if you add one more quantum of energy? A. zero B. 1.40 x 10 -23 J/K C. 1.52 x 10 -23 J/K D. 1.21 x 10 -23 J/K E. 1.63 x 10 -23 J Answer: B ( ) ( ) 1 ! ! 1 ! q N q N + - Ω = - ln S k Ω Answer: A Thermal energy is transferred from coffee to the penny because this brings the system to a more probable state – i.e. the number of possible microstates representing the same macrostate (fixed total energy) increases. Larger number of microstates corresponds to larger entropy. Note that the entropy of the penny rises (more ways to distribute larger number of quanta of energy among penny’s atoms). At the same time entropy of coffee decreases (fewer quanta of energy in coffee). However, the total entropy increases – the rate of change of entropy over energy is higher for the penny, because it had lower temperature (1/T=dS/dE).
3 Problem 3. Consider the mass-spring system as shown. Assume a frictionless surface, a mass m = 4.0 kg, and spring constant k = 100 N/m. The mass is pulled to the right by a distance x=0.3 m from its equilibrium position, and is held at rest. At time t = 0, it is released. In the subsequent oscillations of the mass, what is its maximum speed? A.

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## This note was uploaded on 08/02/2011 for the course PHYS 172 taught by Professor ? during the Spring '08 term at Purdue.

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FinalExam-practice-2010s-answers - PHYS 172 Spring 2010...

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