MT1 - b) Sketch T vs. S for this process. You need not...

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PHYSICS 7B – Fall 2010 Midterm 1, R. Ramesh Monday, September 27, 2010 Use the convention that Δ E=Q-W on this exam. Problem 1 (20 points) Consider a gas being blown along at a velocity u = u ˆ z , so that its velocity distribution is given by F ( v ) = 1 Z e " m ( v " u ) 2 /2 kT . Note that this is a probability distribution for the vector quantity v , not the scalar speed v= |v| , and has units of [velocity] -3 . a) Find v , v 2 and v rms . b) Find the peak velocity where F( v ) is maximized. Problem 2 (15 points) One hundred grams of ice at 0 ° C is dropped into 200g of water at 49 ° C. The system is thermlly isolated. After a period of time, the ice has entirely melted, leaving 300g of water at 6 ° C. Assume the specific heat of water is constant and equal to 1JK -1 kg -1 . a) Calculate the latent heat of fusion for water. b) Calculate Δ S for the entire system. Problem 3 (25 points) For the thermodynamic cycle on the right with an ideal diatomic gas as the working material, a) Calculate W and Q for each of the four sides of the PV diagram.
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Unformatted text preview: b) Sketch T vs. S for this process. You need not indicate specific values of T or S on your plot, but label the points 1-4 corresponding to those on the P-V diagram. c) Compare the efficiency of this engine with the efficiency of a Carnot engine for T H =400 K, T C =300 K, V 1 =1 L, and V 2 =5 L. Problem 4 (15 points) Using what you know about heat conduction, derive equations for the effective thermal conductivity of two materials with the same area and thickness but different thermal conductivities k 1 and k 2 when a) The materials have are arranged in series (heat flows through one then through the other). b) The materials conduct heat in parallel (heat flows through both simultaneously). Problem 5 (25 points) Use a combination of heat engines and heat pumps to prove that no engine can be more efficient than a Carnot engine when operating between a given maximum and minimum temperature....
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