Thermodynamics Problems

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```					                                          Thermodynamics Homework
1989 PHYSICS B THERMO

1. An ideal gas initially has pressure p0, volume V0, and absolute temperature T0. It then undergoes the
following series of processes:

I.     It is heated, at constant volume, until it reaches a pressure 2 p0.
II.    It is heated, at constant pressure, until it reaches a volume 3V0.
III.   It is cooled, at constant volume, until it reaches a pressure p0.
IV.    It is cooled, at constant pressure, until it reaches a volume V0.

(a) On the axes below
i. draw the pV diagram representing the series of processes;
ii. label each end point with the appropriate value of absolute temperature in terms
of T0.

(b) For this series of processes, determine the following in terms of p0 and V0.

i.    The net work done by the gas (answer: -2povo)

ii.   The net change in internal energy (answer: zero for entire cycle)

iii. The net heat absorbed (answer: Q = +2povo) Why? Because Q + W = U and
since U = 0, then Q=-W)

1995 PHYSICS B THERMO

2. A heat engine operating between temperatures of 500 K and 300 K is used to lift a l0-kilogram mass
vertically at a constant speed of 4 meters per second.

(a) Determine the power that the engine must supply to lift the mass. (answer: 400 watts)

(b) Determine the maximum possible efficiency at which the engine can operate. (answer: 40%)

(c) If the engine were to operate at the maximum possible efficiency, determine the following.

i.   The rate at which the hot reservoir supplies heat to the engine (answer: 1000 Watts)

ii.The rate at which heat is exhausted to the cold reservoir (answer: 600 watts)
1996 PHYSICS B THERMODYNAMICS

3. The inside of the cylindrical can shown above has cross-sectional area 0.005 m2 and length 0.15 m. The
can is filled with an ideal gas and covered with a loose cap. The gas is heated to 363 K and some is allowed
to escape from the can so that the remaining gas reaches atmospheric pressure (1.0 x 105 Pa). The cap is now
tightened, and the gas is cooled to 298 K.

(a) What is the pressure of the cooled gas? (answer: 8.2 x 10 4 pa)

(b) Determine the upward force exerted on the cap by the cooled gas inside the can.
(Mr. Young hint: Pressure = Force/Area of cap) (answer: 410 N)
(c) If the cap develops a leak, how many moles of air would enter the can as it reaches a final
equilibrium at 298 K and atmospheric pressure? (Assume that air is an ideal gas.) (answer:
0.0054 moles)
1999 PHYSICS B7

4.
A cylinder contains 2 moles of an ideal monatomic gas that is initially at state A with a
volume of
1.0 X 10-2 m 3 and a pressure of 4.0 x 105 Pa. The gas is brought isobarically to state B, where the volume
is 2.0 x 10-2 M3 . The gas is then brought at constant volume to state C, where its temperature is the same
as at state A. The gas is then brought isothermally back to state A.

(a)              Determine the pressure of the gas at state C. (answer: 2 atm or 2 x 105
pa)

(b) On the axes below, state B is represented by the point B. Sketch a graph of the
complete cycle. Label points A and C to represent states A and C, respectively.

(c) State whether the net work done by the gas during the complete cycle is positive,

(d) State whether this device is a refrigerator or a heat engine. Justify your answer.

Next page has more problems…. Scroll down!

Don’t skip these next problems! They are the ones you’ll most likely find on the
Multiple Choice section of our exam.

5. What is the shape of a line on a P-V graph along an isotherm?
a. hyperbola b. straight horizontal line c. straight vertical line

6. What is the shape of a line on a P-V graph along an isobar?
a. hyperbola b. straight horizontal line c. straight vertical line

7. What is the shape of a line on a P-V graph along an isochoric process?
a. hyperbola b. straight horizontal line c. straight vertical line

8. What is the first law of thermodynamics: In words and give a useful analogy.
9. What is the first law of thermodynamics: in it's mathematical form, and state what
each variable stands for.

10. Circle the process in which U is zero (isothermal, isochoric, isobaric, adiabatic)
11. Circle the process in which Q is zero (isothermal, isochoric, isobaric, adiabatic)
12. Circle the process in which W is zero (isothermal, isochoric, isobaric, adiabatic)

13. Which are state functions (there are 2)
a. S   b. Q      c. W     d. U

14. What's the difference between a state function and one that is not a state function.

15. What are the units for Q, W and U? (hint, they're all the same unit!)

16. What are the units for S?

17. If a gas doesn't expand or compress, has any work been done? (yes or no)

18. What's another word for "disorder"? (starts with an "E")

19. Name four things the second law of thermodynamics applies to in a practical sense
(look at my notes on "practical applications of the second law").

20. What is the mathematical formula to find S.

21. True or False: S along an adiabat is zero

22. True or False: S along the Qhot isotherm is equal to the S along the Qcold isotherm

23. Which is positive and represents endothermic heat
a. Qhot       b. Qcold
24. A Carnot Cycle consists of ____________________ (name the four lines which
form the Carnot Cycle on a P-V graph.

25. How can you find the total work done in a cycle on a P-V graph?

26. What is the change in internal energy of a cycle on a P-V graph if the cycle begins at
point A and ends back at point A (and it doesn't matter the processes you took to go from
A back to A again.

Finding Change in Internal Energy (U):
The key to getting these is correctly assigning the +/- signs to the Q and W values
and then adding them up to find U. Refer to my hints above so you can quickly
assign + or – values to each Q and W value
U = Qnet + Wnet (and “net” is a fancy way of saying, add „em up!)

I have included the answers for quick reference. (they ask these frequently on the
Multiple choice section of the test. They are usually missed by students, but as you
can see, they are quite simple if you just know the method)

27. A gas in a container absorbs 200 J of heat and has 100 J of work done on it, and it
then does 15 J of work. What is the increase in internal energy of the gas?

28. In a particular process, 400 J of heat is released from a system and the system
simultaneously has 100 J of work done to it. What is the change in internal energy?

29. A gas releases 200 J of heat when it is compressed and then absorbs 500 J more heat
to re-expand itself. During this process the expanding gas did 100 J of work and the
compression of the gas had 450 J of work done on it. What is the change in internal
energy?

Finding Efficiency:
e = Wnet/QH = TH-TC/TH = QH-QC/QH (notice that Wnet = QH-QC)

30. In each cycle of a Carnot engine, 100 J of heat is absorbed from the high-temperature
reservoir and 40 J is exhausted. What is the efficiency of the engine?

31. An engine operates between a temperature of 1000 K and 500 K. What is the
efficiency of the engine?

32. A heat engine draws 800 J of heat from its high-temperature source and discards 450
J of exhaust heat into its cold-temperature reservoir during each cycle.
a) How much work does this engine perform per cycle? (Answer: +350J)
b) What is its efficiency? (answer: 43.75%)
(Hint: Wnet = QH-QC)
(another hint: Pretend your “heat engine” is your car. You put in 800 J of heat from the
gasoline burning in the cylinder and 450 J of heat is exhausted and not used by the engine
to help make the car run. That means the engine used +350 J of energy to actually run the
car. When an engine does work on something else, it is Positive.)

33. A heat engine has an efficiency of 70%. If 1000 J of energy is provided to this
engine, how much heat is lost? (answer: 300 J)
34. True or False: Slow expansions of gasses (or slow compressions of gasses) allow for
a change in temperature. (answer: FALSE. If they go slowly, they lose heat to the
surroundings – or gain it. Only FAST expansions/compressions do this. Those are called
“adiabatic”. Slow ones are called “isothermal”).

Finding S Problems:
35. Find the change in entropy of 10.0 g of water that freezes into ice at 0oC. The latent
heat of fusion of ice is 334.4 KJ/Kg.
(hint: 334.4 KJ/Kg is the same thing as 334.4 J/g. The Kilo's cancel!!!!!)
(answer: -12.25 J/K. Notice that the answer is negative, because S is becoming more
ordered when water freezes into ice)

36. Find the change in entropy of 10.0 g of water that boils into steam at 100oC. The
latent heat of vaporization of water is 2257 KJ/Kg.
(answer: +60.5 J/K. Positive because steam is more disordered than water)

Just some general notes that you should be aware of too:
You should also know that heat transfer between two objects is FASTER if they have large
surface areas touching and SLOWER if they are large objects. Example, imagine two thin, long
metal pipes touching and trying to transfer heat, it will take forever. But, imagine two fat short
metal pipes touching. Much shorter time to transfer heat. Again, your grandmother could love
this problem. They love to ask this problem: Time varies as A and 1/L. Meaning, it is faster
with a big area and slower with a long length.

Oh, and a couple more things about heat and metals:

-To be in thermal equilibrium means that they are at the same temperature. For example: If two
metals are in thermal equilibrium with each other and one has a temperature of 300 K, then the
other one has what temperature? (Answer: 300 K). NO MATTER WHAT TYPE OF METALS
THEY ARE! One could be AL, the other AU, doesn‟t matter.
-If you have a metal plate with a hole in the center of it and you heat the metal plate, the hole in
the center of the plate will EXPAND (get bigger). This happens with rings too!

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