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    Work and Energy - Volume, Pressure and Temperature

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    1. You have a 16 oz cup of coffee at 180 degrees F. That is way too hot to drink. So you want to cool the coffee off and decide to add some cold water. You add 2 ounces of cold water at 40 degrees F. How much will the water you added heat up? How much will the coffee that you poured the water into cool down?

    2. An air bubble at the bottom of a lake has a volume of 15 cm3. The lake is 40 m deep and has a temperature of 4 C at the bottom. The bubble then rises to the surface where the temperature is 23 C. What is the volume of the bubble just before it reaches the surface?

    3. You are sitting behind a curtain watching meters that measure pressure, volume, and temperature of some kind of heat engine. Pressure, volume, and temperature have reached an equilibrium state. Then someone behind the curtain tells you that they are going to add energy to the system. The energy is added and the equilibrium changes. Can you tell whether they did work on the system, heated the system, or a combination of both? Explain your answer.

    4. In a refrigerator, heat is transferred from a colder area (the inside of the refrigerator) to a warmer area (the air outside of the refrigerator). Given what you know about internal energy, explain how this is possible.

    In answering the problems, assume that the density of water is about 62 lb/ft3.

    5. A pipeline has an entrance diameter of 2 ft. and an exit diameter of 1 ft. Water flows into the entrance of the pipe at 100 ft/sec. The pressure at the entrance is 200 lb/ft2. Find the velocity and pressure at the exit. (Assume that there is no friction.)

    6. A buoyant object is submerged in water. The buoyant force is measured at 5 lb-ft/sec2. When weighed in the open air, the ball weighs 3 lb. (Remember that open air weight is equal to mass times gravity.) What is the density of the ball?

    7. You want to compute the values of the water pressure at various depths below the surface of a lake. Compute the water pressure at 50 feet below the surface, 100 feet below the surface, and so on down to 500 feet below the surface. Show the results of your calculations in a table.

    Answer the following four related questions:
    8. How is the speed that an airfoil (i.e. a wing) is traveling over the top and bottom surfaces related to the pressure that is exerted on the top and bottom surfaces of the wing?
    9. How is the total pressure resolved into lift and drag.
    10. How does drag affect the velocity of the wing?
    11. How is the height that the airfoil will rise to affected by the weight of the airfoil?

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    Solution Summary

    This solution is provided in 617 words in an attached .doc file. It uses step-by-step equations to solve each question. The relationship between pressure, volume and temperature are also discussed. A graph is included to help understand the relationship between pressure and depth.