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Final-solutions 1 - PHYSICS 222 Section 1 Dr Yost Final...

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PHYSICS 222 Section 1 Dr. Yost Final Exam Solutions 1. [15pt] Suppose 7.9 moles of Helium, a monatomic ideal gas, at a temperature of 28 o C is placed in a piston with an initial volume of 2.2 m 3 . (a) [5pt] If the piston expands isothermally to a final volume of 7.4 m 3 , how much work is done by the gas? (b) [5pt] What is the final pressure of the helium? (c) [5pt] What is the change in entropy of the gas in the expansion process? For an isothermal process, so by the definition of entropy,
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2 2. [10pt] A total of electrons (each with charge C) are placed uniformly along an initially un- charged wire of length 2.32 m. (a) [6pt] What is the magnitude and direction of the electric field a perpendicular distance 1.69 cm away from the midpoint of the wire? [You may treat the wire as infinitely-long, if it helps.] It is a good approximation to treat this as an infinite line charge. Applying Gauss’s Law to a cylinder of radius and length surrounding the wire gives The sign means that the electric field points inward, toward the wire. For the coordinates shown, An exact solution can be obtained by integrating the field produced by each small element of the line charge. By symmetry, and Here, is the angle shown in the figure, and is its maximum value. (b) [4pt] What is the magnitude and direction of the acceleration of a proton at that point, if it is free to move? (A proton ’s mass is kg, and its charge is .) 1.69 cm 2.32 m
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3 3. [15pt] A 12.0 V battery is attached to a 5.25 mF capacitor and a 3.60 k resistor as shown. (a) [5pt] If the capacitor was initially uncharged when the switch was first closed, how long does it take to reach 90% of its full charge? The time-constant is The current is with so the charge on the capacitor is When the capacitor is 90% charged, , so (b) [5pt] What energy is stored in the capacitor once it is fully charged? (c) [5pt] How much energy was converted to heat in the resistor during the complete charging process? The energy supplied by the battery was so the energy converted to heat in the resistor was + ……… . 12.0 V 5.25 mF 3.60 k
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4 4. [4pt] The figure shows the cross section of a long, solid, cylindrical conductor. The radius of the cylinder is cm. A current of 1.31 A is uniformly distributed (constant current density) through the conductor and is flowing out of the page, in the direction.
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