PHY 126-07 Final Exam

1. PHY 126-07 Final Exam A small ball of mass 2.00 kg is suspended by two wires, wire 1 and wire 2. If two wires make 90o and wire 2 makes q=30o with respect to the vertical, find the tension T1 and T2. Q P wire 2 q= 30o wire 1 90o T2 Problem 1 (20 points) T1 mg

2. Problem 2 (10+10 points) An innovative musician is making a new musicinstrument using cylindrical glasses of height h=1 m with some water in them where the top (bottom) of each glass is open (closed). Right now he is adjusting the height of the water in one of the glasses so that sound of middle C note at frequency 256 Hz creates resonance. Assume that the speed of sound is 344 m/s. (a) What is the maximum height of water for the instrument to resonate with middle C note? (b) What is the next lowest frequency of sound that this glass instrument can resonate with if the water level is the same as in Part (a). open L water h closed

3. Problem 3 (20 points) Jane and John will host a big party. They are preparing iced tea for the party. Their plan is to have iced tea at 3.0oC in an insulated container without ice left in it. They first made 15 liters of tea at 20oC. Then they plan to put some ice at -5.0oC into the container to cool the tea. How much of ice is needed to make this iced tea according to their plan? Treat the tea as water. If needed, use the following constants: the density of water rwater=1000 kg/m3, the latent heat of fusion of water Lf=3.33 x 105 J/kg, specific heat of ice cice=2090 J/(kg K) and the specific heat of water cwater=4190 J/(kg K).

4. Problem 4 (5+5+5+5 points) You are experimenting with a converging lens with a focal length of 10 cm. Find the image position (whether on the left or right of the lens and how far from the lens), magnification, and whether the image is upright or inverted, and real or virtual when an object is placed at (a) 25 cm, (b) 10 cm, (c) 7.5 cm and (d) -20 cm. If the image is formed at infinity, just stating that gets you 5 points. Assume that the incoming light rays come from the left of the lens toward the lens.

5. An experimental power plant at the Natural Energy Lab generateselectricity from the temperature gradient of the ocean. The surface anddeep-water temperatures are 27oC and 6oC, respectively. (a) What is the maximum theoretical efficiency of this power plant? (b) If the power plant is to produce 210 kW of power, at what rate mustheat be extracted from the warm water? (c) If the power plant is to produce 210 kW of power, at what rate mustheat be absorbed by the cold water? (d) To raise the temperature of water whose mass is dm by DT, how muchof heat dQ is needed? (For this question you may use the symbol c for specific heat of water). (e) The cold water that enters the plant leaves it at a temperature of 10oC. What must be the flow rate of cold water through the system in kg/h? Problem 5 (5+5+5+5+5 points) [Use, if needed, the fact that specific heat of water is c=4190 J/(kg K)].

6. Problem 6 (3+3+3+3+3+3+2 points) • Three moles of an ideal gas are taken around the cycle acb shown in Figure. For this gas • Cp = 29.1 J/(mol K). Process ac is at constant pressure, process ba is at constant volume, • and process cb is adiabatic. The temperature of the gas in states a,c, and b is Ta=300 K, • Tc=492 K, and Tb=600 K. The universal gas constant R is 8.31 J/(mol K). • For a process at constant pressure, when the temperature changes by DT, how much • does the volume change DV? • For process ac, how much work is done (plug-in numbers)? • For an ideal gas, find the molar heat capacity at constant volume CV in terms of Cp and • the universal gas constant R (no numbers). • (d) For process cb, how much is the change of internal energy, DU in terms of the number of • moles n, CV, and the change of temperature DT (no numbers)? • (e) For process cb, how much work is done (plug-in numbers)? • For process ba, how much work is done (plug-in numbers)? • Find the total work done for the cycle acba? p b a c O V