Fa08-MT1-SunRev1-Probs

Fa08-MT1-SunRev1-Probs - cost to cool your house for one...

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Physics 7B, Fall 2008 MT 1 - Sunday Review, Part 1 Nicole Carlson 1. a) Draw a Carnot cycle in the T - S plane. b) What does the area within the curve represent? 2. Suppose you have an engine that operates using a diatomic ideal gas on the Sterling cycle. The Stirling cycle consists of two isotherms connected by two vertical isochors. Let’s suppose that V 2 = 2 V 1 for fun, and leave the rest of our work in terms of T 2 and T 1 , where the temperature T 2 > T 1 . a) Find the efficiency of your Stirling cycle in terms of the Carnot efficiency. b) How does your Stirling efficiency compare to the Carnot efficiency? c) Now assume that you can reverse the direction of your cycle to use it as an air conditioner to cool your home. On a cold day (with your Stirling air conditioner OFF), the house requires 5 kW of heat when it is 13 ° C outside and 21 ° C inside. If the cost of electricity is $0.14 per kW-hr, how much does it
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Unformatted text preview: cost to cool your house for one month with your Stirling air conditioner if its 37 C outside and you still want to keep it 21 C inside? 3. A binary alloy is made by mixing atoms of two distinct substances A and B in equal parts. The total number of atoms in this allow is N . a) What is the entropy of this system if N = 10 23 ? (You may assume that ln( n !) n ln n ) b) The entropy that is created in making the alloy is called the mixing entropy . If no work was required to mix the alloy at 300K, evaluate the change in internal energy for the alloy. c) How would your results change if A and B were not distinct? 4. For the gas speed distribution of N particles, f ( v ) = Cv 2 for 0 < v < v max and f ( v ) = 0 for v > v max , find: a) C in terms of N and v max . b) The average (mean) speed of the particles. c) The rms speed of the particles....
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