Midterm2006

Midterm2006 - VERSION A 1(20 points PART I SHORT ANSWER(a(5...

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Unformatted text preview: VERSION A 1. (20 points) PART I: SHORT ANSWER (a) (5 points) Sketch the electric field lines for 2 equal positive point charges. + + (b) (5 points) If hot air rises, why is it cooler at the top of a mountain than at sea level? Answer: As the air rises, it expands, pushing away the surrounding air and doing work. As a result, its internal energy decreases and it cools. Recall that for an ideal gas E int = nC V T which shows that the internal energy is proportional to the temperatures. 1 (c) (5 points) The speeds of 5 molecules are 2.0, 3.0, 4.0, 5.0, and 6.0 km/s. What is the their root-mean-square speed v rms ? Show your work. Answer: v 2 = 1 5 X i v 2 i = 1 5 2 2 + 3 2 + 4 2 + 5 2 + 6 2 km 2 / s 2 = 18 km 2 / s 2 v rms = √ v 2 = √ 18 km / s = 4 . 24 km / s (1) v rms = 4 . 24 km/s 2 (d) (5 points) In the PV (pressure-volume) diagram, the ideal gas does 5 J of work along the isotherm ab , and it does 4 J of work along the adiabat bc . (In other words, going from a to b is an isothermal process, and going from b to c is an adiabatic process.) What is the change Δ E int in the internal energy of the gas if the gas traverses the straight path from a to c ? Be sure to get the sign right. Explain your answer. p V c b a Answer: Along ab , T = constant. For an ideal gas, E int = nC V T . So if the tem- perature is constant, E int is constant and Δ E int = 0 along ab . Along bc , Q = 0. From the first law of thermodynamics, Δ E int = Q + W = W =- 4 J where W is the work done on the system. We have a minus sign because work is done by the system. Since the change in internal energy is independent of the path taken, Δ E int =- 4 J. Δ E int =- 4 J 3 PART II: WORK OUT PROBLEMS 2. (20 points) (a) (15 points) A cylindrical bucket hangs above the ground. The radius of the bucket is R 1 = 25 cm and it is filled with water to a depth of h = 50 cm. A hole of radius R 2 = 0 . 5 cm is poked in the center of the bottom of the bucket. What is the initial speed v at which the top of the water in the bucket falls? Show your work....
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This note was uploaded on 09/08/2008 for the course PHYS 3B taught by Professor Wu during the Winter '08 term at UC Irvine.

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Midterm2006 - VERSION A 1(20 points PART I SHORT ANSWER(a(5...

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