midterm1_solutions - University of South Carolina...

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University of South Carolina Department of Physics and Astronomy Phys 706, Thermodynamics and Statistical Physics. Midterm # 1 February 21, 2011 The test is open book/notes. You can use any materials you like. If you need extra paper or you forgot a calculator – please ask. There are 3 problems, each worth 10 points. It is enough to solve one problem to get a full credit. Choose any one you like. If you solve more, you will get extra credit. If you have a question about the problem’s formulation – please do not hesitate to ask. I will either answer your question or will tell you that I cannot do it without revealing the solution. Your solutions should have a readable form showing the flow of argument. You have to be able to express yourself in writing. Writing skills are important for any scientist. They are not just making your solutions look nicer. If you cannot explain yourself clearly, you probably do not understand what you are doing. You can still try to guess the answer for a problem. If the solution is a number or an expression, I will accept your answer (guessing will not be accepted for problems where the answer is “yes” or “no”). However, if no explanations are given, only correct answers will be graded positively. There will be no partial credit in the absence of correct, readable explanations. GOOD LUCK! 1 Evaluation of an invention After Albert Einstein leaves his position at the Patent Bureau in 1908, you are hired to replace him. Shortly, an inventor shows up at the office with the drawings of a refrigerator. He claims that the machine will cool 1 liter of water from the room temperature of 300 K down to 280 K using just 2,000 Joules of the newly invented electric power. The refrigerator itself is at room temperature in the beginning of the process. The specific heat capacity of water is c = 4200 J/kg K. Using thermodynamics, calculate the lower bound for the amount of work needed to perform the cooling. Should you grant a patent to the inventor?
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