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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.

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See Also This Related BrainMass Solution

Total of twenty questions related to work, energy, power, simple pendulum, electricity, electric power, gravitational potential energy, kinetic energy ,Celsius temperature, Kelvin temperature, specific heat, heat and Ideal gas law.

1. A force of 7.2 N acting on a 1.0-kg object initially at rest moves it through a parallel distance of 2.5 m. How much work is done on the object?

2. Neglecting friction, what is the speed of the object in Question 1 when it has moved 2.5 m?

3. A 0.10-kg ball is dropped from a height of 10 m and rebounds to a height of 8.0 m. How much energy was lost, and what happened to it?

4. A student weighing 700 N climbs a flight of stairs 5.0 m high. Calculate the work done.

5. If the student in Question 4 climbs the stairs in 10 s, what power was required?

6. The bob of a simple pendulum is 0.50 m above the floor at its lowest position. Calculate the maximum speed of the bob when it is held at a maximum height of 2.5 m and released.

7. Given 10 kWh of electricity and assuming no losses, how much work, in joules, could be done?

8. A 5.00-kg object is lifted from the floor to a shelf. The object's new gravitational potential energy relative to the floor is 102 J. What is the height of the shelf?

9. Work in the amount of 280 J is done in lifting an object a distance of 4.0 m in a time of 7.0 s. How much power was required?

10. Car B is traveling twice as fast as Car A, but Car A has twice the mass of Car B. Which car has the greater kinetic energy and by what factor?

11. It is 23 ° F outside. What is the Celsius temperature?

12. For a temperature of − 40 ° F, what are the corresponding temperatures on the Kelvin scale?

13. When 10 kcal of heat is added to 2.0 kg of a substance, its temperature increases 20 C ° . What is the specific heat of the substance?

14. How much heat is required to melt 5.0 kg of ice at 0 ° C to water at 0 ° C?

15. How much heat is necessary to change 20 g of ice at − 10 ° C into water at 20 ° C?

16. How many kcal of heat would be needed to melt 0.12 kg of ice at 0 ° C and increase the temperature to 25 ° C?

17. A constant volume and mass of helium gas at 27 ° C is heated so that the pressure of the gas doubles. What is the new temperature of the gas in degrees Celsius?

18. The number of molecules in a container is tripled and the Kelvin temperature doubled. The volume remains unchanged. The new pressure will be how many times greater than the original pressure?

19. An ideal gas is confined to a container with an adjustable volume. If the number of molecules and temperature are held constant, by what factor will the volume change when the pressure is tripled?

20. The piston of a cylinder containing a quantity of ideal gas is advanced so that the volume of the gas is decreased by one-half. A pressure gauge on the cylinder shows the pressure of the gas to have increased threefold in the process. By what factor does the temperature of the gas change?

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