Pre AP Physics Chapter 11: Thermodynamics Problems

Problems (210)

Solve the problems below on your own paper. Each problem must be solved on its own page. Be sure to use the 3-column method. Naturally, you are encouraged to use your formula/equation sheet. be sure that your boxed solutions are clearly marked with 'a', 'b', or 'c' etc. Be aware that some responses will be in complete sentences rather than in the 3CM.

1. A large cylinder with a diameter of 36 cm must ush aganist one atmosphere of pressure. the cylinder accomplishes this by doing 1236.2 J as it moves 12 cm.

a) Calculate the change in volume of the cylinder.

b) Calculate the pressure of one atmosphere in Pascals.

c) Convert your answer to kilopascals.

2. During an adiabatic process a gas decreases its internal energy by 500 J.

a) How much energy is transferred as heat in this process? Explain how you know.

b) How much, if any, work is done in the process? Explain how you know.

c) Is the work, if done, done on or by the gas? explain how you know.

3. A machine takes in 1.127 x 10⁴ kJ of energy and expells 9.58 x 10³ kJ of energy, doing work inbetween.

a) In a world of round cows, how much work does this machine do?

b) What is the ideal efficiency of this machine?

4. An engine with an efficiency of 23% loses 627 J of energy during each cycle.

a) How much energy as heat must this engine have at the start of each cycle in order to run?

b) How much work can this engine do?

c) What sort of change can an engineer make to this engine so that it can be more efficient?

5. An engine gives 500 J of wotk at an efficiency of 27%.

a) Solve the equation for efficiency in terms of ‘Q’ for Q_L.

b) Write the efficiency equation again in terms of work and Q_H. Solve this for Q_H.

c) Combine the equations from part ‘a’ and ‘b’ and calculate Q_L.

d) Calculate Q_H.

6. On a 650 km trip to Lubbock this coming May 21 to see the annular eclipse fo the sun the tires of Mr. Young’s Rav-4 got hot enough to change their volume from 33.3 x 10^-3 m³ to 40.2 x 10^-3 m³. The tire pressure, of course remained constant at 260 kPa.

a) How much work was done?

b) Was this work done on or by the tires? Explain how you know.

7. Mr. Young used a pressure cooker to make is New Year’s black-eyed peas. In the PC are the peas with onions, spices and water. Some of the water is vaporized at a temperature higher than 100 ⁰C so that the peas cook a lot faster. 9273 J of energy was added to the PC in order to accomplish this.

a) What happened to the water’s internal energy as it vaporized? Explain how you know.

b) In order to vaproize the water at constant temperature was energy added to or taken away from the system? Explain how you know.

c) In order for the water to vaporize how much energy as work, if any, was added to the system? Explain how you know.

d) Calculate the change in the internal energy of the system. Use the 3CM.

Pre AP Physics Chapter 11: Thermodynamics Problems

Answer Section

PROBLEM

1. ANS:

a) The change in volume is simply the area of the cylinder multiplied by the distance the cylinder moved: .

So,

Work this out in the 3CM.

b) Work, of course is so

Do this in proper 3CM format.

c) Your answer in part ‘b’ should be a six digit number (not counting the two decimal points). To convert this to kilopascals simply move the decimal point three places to the left.

Your answer should be 101.327 kPa.

2. ANS:

a) Since the process is adiabatic there is no energy transferred a heat. Q = 0.

b) The equation: tells us that the magnitude of the work is equal to the change in the internal energy. Be sure to work out ‘b’ in the 3CM.

c) A careful examination of the equation reveals that the change in internal energy is negative! This means that the equation actually looks like this: . This means that the work done is positive. When work is poisitive the change in volume is also positive which means the gas expanded into its environment. The gas, in other words, did work on the environment so the work is positive.

3. ANS:

a) Useing the 3CM this equation will get you the work done by the machine in a cows are round workd: .

b) Use the equation in the 3CM to find the ideal efficiency. Write your answer as a percent.

4. ANS:

a) The 627 J is the Q_L for this engine, so use the efficiency equation and then solve it for Q_H:

and

b) To find the work this machine can do use

c) To increase the efficiency of the machine an engineer might find a way to increase the Q_H of the machine. The Q_L is usually the environment and this is difficult even for an engineer to change.

5. ANS:

a) so

b) so

c) Now we can make an equation for which we have all of the variables:

d) To find Q_H simply use the equation and solve for Q_H..

6. ANS:

a) Of course you will first find the change in volume by subtracting the smaller volume from the larger volume and then use this equation: .

b) If the work is positive the tires died work on the environment. If the work is negative it is the other way round.

7. ANS:

a) As the water vaporizes its internal energy increases. I know this because water vapor has more internal energy than liquid water at the same temperature since vapor consists of very fast moving particles while liquid water has only slowly moving particles.

b) In order for the water to vaporize energy as heat must be added to the system. I know this because if no energy was added nothign would have happened.

c) There was no energy as work added to the system. I know this because when the energy was added to the system the volume remained constant. In an isovolumetric process, such as this, no work is done.

d) The first column should reflect that work is equal to zero and Q is equal to 9273 J. The middle column should have the equation . Since work equals zero, the chnage in internal energy must equal the energy as heat that was added to the system. This should be reflected int eh third column.