AP Physics B
Lesson 16.a Thermodynamics
Outcomes
1. Determine the work done on or by a confined ideal gas.
2. Apply the First Law of Thermodynamics to solve problems involving idealized
Carnot Cycles.
3. Determine the efficiency of a heat engine.
Name
∆U=±Q±W
PV=nRT
U=3/2 nRT
[(TH-Tc)/TH]•100=e
Date
Period
Engage
1. What happens to the potential energy of this mass?
2. What has to be exerted on the mass in order for this to occur?
3. Where does this energy come from?
4. What happens to the potential energy of this mass?
5. What has to be exerted on the mass for this to occur?
6. Where does this energy come from?
7. What are the final units of this calculation?
p  V  Pascals m3 
Nm
?
m2
3
8. What do those units represent?

9. When a change in volume occurs for a confined gas at constant pressure,
what does the gas do on the external environment?
10. What impact do you think this would have on the internal energy of the
confined gas, if the gas expands?
11. What impact do you think this would have on the internal energy of the
confined gas, if the gas is compressed?
Explore I Build a Heat Engine (We will do this when I get back; for right now assume that the
chemical energy of the peanut is transformed into thermal energy of the boiling water; the
steam will push the mass sitting on top of the plunger higher; see the energy transformation
diagram below)
• Construct a heat engine using the provided materials (place a
small amount of water in the test tube).
• Use and electronic balance to determine the mass of the object
you place on top of the piston.
• Ignite the peanut using a match.
• Measure the change in height experienced by the mass.
• Determine the change in potential energy experienced by the
mass.
• Determine the work done on the mass.
• Determine the heat added to the water (assume 100%
conversion to mass GPE)
Explain I
14. Complete the energy transfer diagram for the event. Use the terms Work, Chemical Potential Energy, Gravitational Potential
Energy, Heat, and Internal Energy
Chemical Potential
Energy
Gravitational Potential
Energy
Internal Energy
Heat
15. What does a heat engine do?
16. What kinds of things could be done to improve the efficiency of this heat engine?
17. Give two examples of heat engines in the real world.
Work
Explore II – Notes
I. Heat Engine
A. A device that converts thermal energy
into mechanical energy.
B. First Law of Thermodynamics
1. ∆U=±Q±W
anything done to the gas is
considered positive
II. Thermal Processes
A. Isobaric Transformation
18. Compare the input thermal energy temperature with the output thermal energy
temperature.
Input thermal energy is at a higher temperature
19. What is the difference in the input thermal energy and the output thermal
energy equal to?
Work Out Qin – W=Qout
20. Given this schematic describing the basic operation of a heat engine, is it
possible to have a heat engine work at temperatures below room temperature?
Yes
21. What does the variable U represent?
Internal energy = ∑ of all molecular kinetic plus potential energies in a sample. In
monatomic gas this would be equal to the kinetic energy based on the translation
of individual gas atoms only.
22. What does the variable Q represent?
Heat
23. What does the variable W represent?
Work
24. What does a + U represent?
Internal Energy is increasing
25. What does a + Q represent?
Heat increasing – Heat is added to the system
26. What does a +W represent?
Work done ON the gas compressing it
24. What does a - U represent?
Internal Energy is decreasing
25. What does a - Q represent?
Heat being taken away from the system
26. What does a -W represent?
Work done by the gas on the external environment through expansion
27. What does isobaric mean?
Constant or same pressure
28. What equation is used to determine the work done on or by an isobaric gas as
is volume changes?
W=p•∆V
W=p(V2-V1)
Joules!!!!
29. What geometric calculation is performed to determine the work done on or by a
gas?
Area P•∆V is an area calculation!!!
30. If work is done by the gas on the external environment, does this increase or
decrease the internal energy of the gas?
Decrease!
31. If work is done on the gas by the external environment, does this increase or
decrease the internal energy of the gas?
Increase!
32. What sign convention is used to represent work done by the gas?
(-)
33. What sign convention is used to represent work don on the gas?
(+)
34. In order for a transformation to remain isobaric as a gas expands, what must be
added to the gas? (Sign Convention?)
+ Q Heat must be added!!!!
35. In order for a transformation to remain isobaric as a gas contracts, what must be
removed from the gas? (Sign Convention?)
- Q Heat must be removed!!!
36. How would you write the First Law Equation for an Isobaric Expansion?
∆U=+Q-W
37. How would you write the First Law Equation for an Isobaric Compression?
∆U=-Q+W
B. Isometric Transformation
38. What does isometric mean?
Same volume – no change in volume – (Isochoric, Isovolumetric)
39. What is the work done during any isometric transformation?
O None, Nada, Mayo, No, No, NO WORK DONE!!!!
40. If the pressure increases during an isometric transformation, what
happens to the internal energy of the gas?
It increases ∆U is + positive
41. If the pressure decreases during an isometric transformation, what
happens to the internal energy of the gas?
It decreases ∆U is – negative
42. How would you write the First Law Equation for an isometric
transformation where the pressure increases?
∆U=+Q
43. How would you write the First Law Equation for an isometric
transformation where the pressure decreases?
∆U=-Q
44. What is the sign convention for the heat transferred to a gas during an
isometric transformation where the pressure increases?
+Q
45. What is the sign convention for the heat transferred to a gas during an
isometric transformation where the pressure decreases?
-Q
C. Isothermal Transformation
46. What is an isothermal transformation?
Constant Temperature
47. How does the internal energy of the gas change during an isothermal
transformation?
It DOESN’T!!!!!! No ∆T means No ∆U
48. What equation supports this statement?
U=3/2nRT
49. How does the work done on or by the gas compare to the heat added to
or removed from the gas in an isothermal transformation?
∆U = 0 ∆Q=∆W
49. How would you write the First Law Equation for an isothermal
transformation where the gas expands?
0=+Q-W
50. How would you write the First Law Equation for an isothermal
transformation where the gas is compressed?
0=+W-Q
51. What geometric /mathematic process would you use to determine the
work done on or by the gas during an isothermal transformation?
AREA - Calculus
52. How else could you determine the work done on or by the gas?
∆Q=∆W
D. Adiabatic Transformation
53. What is an adiabatic transformation?
54. What factor affects the internal energy of a gas during an adiabatic
transformation?
55. If the gas expands during an adiabatic transformation, what will happen to
the internal energy of the gas?
56. If the gas contracts during an adiabatic transformation, what will happen to
the internal energy of the gas?
57. How would you write the First Law equation for an adiabatic transformation
when the gas expands?
58. How would you write the First Law equation for an adiabatic transformation
when the gas contracts?
III. An Actual Heat Engine Moving through Gas Transformations
IV. An Idealized “Carnot” Cycle
59. What is the net work done by a
gas on the external environment for
one complete cycle?
60. What is the total change in
internal energy of the gas for one
complete cycle?
V. An Air Conditioner
61. How is an air conditioner
different than a heat engine?
62. Is mechanical work obtained
from the thermal reservoirs related
to an air conditioner?
Explain II
Complete the Following Table with Equations or Variables or + or - Signs
Type of
PV Graph Sketch
Definition of
Transformation
Transformation
Isobaric
Volume Increase
Isobaric
Volume Decrease
Isometric
Pressure Increase
Isometric
Pressure Decrease
Isothermal
Volume Increase
Isothermal
Volume Decrease
Adiabatic
Volume Increase
Adiabatic
Volume Decrease
63. How does a heat engine work?
64. How is the efficiency of a heat engine determined?
∆U =?
Q=?
W=?
I.
II.
1.5 moles of an ideal gas are taken through the idealized Carnot
Cycle shown above.
2 moles of an ideal gas are taken through the idealized Carnot
Cycle shown above.
A. What is the volume of the gas at B?
A. What is the volume of the gas at B?
B. What is the internal energy of the gas at B?
B. What is the internal energy of the gas at B?
C. What kind of transformation is BC?
C. What kind of transformation is BC?
D. What is the internal energy of the gas at C?
D. What is the internal energy of the gas at C?
E. How much heat is added to the gas during the process BC?
E. How much heat is added to the gas during the process BC?
F. What kind of transformation is CD?
F. What kind of transformation is CD?
G. What is the volume of the gas V2?
G. What is the volume of the gas V2?
H. How much work is done by the gas during process CD?
H. How much work is done by the gas during process CD?
I. What is the temperature of the gas at D?
I. What is the temperature of the gas at D?
J. What is the internal energy of the gas at D?
J. What is the internal energy of the gas at D?
K. How much heat was added to the gas during process CD?
K. How much heat was added to the gas during process CD?
L. What kind of process is DA?
L. What kind of process is DA?
K. What is the work done by the gas during the process DA?
K. What is the work done by the gas during the process DA?
M. What is the change in internal energy during DA?
M. What is the change in internal energy during DA?
N. Is heat added to or removed from the gas in process DA?
N. Is heat added to or removed from the gas in process DA?
O. What is the work done on or by the gas during process AB?
O. What is the work done on or by the gas during process AB?
P. What is the change in internal energy for process AB?
P. What is the change in internal energy for process AB?
Q. How much energy is added to or removed from the gas in
process AB?
Q. How much energy is added to or removed from the gas in
process AB?
R. What is the net work done by he gas for one complete cycle?
R. What is the net work done by he gas for one complete cycle?
S. What is the net change in internal energy for the gas for one
complete cycle.
S. What is the net change in internal energy for the gas for one
complete cycle.
III.
An ideal gas experiences the transformations shown above.
A. How many moles of gas are present in the system?
B. What is the temperature of the system at locations: 2, 3, 4?
C. What is the internal energy of the system at locations: 1, 2, 3,
4?
1983B4. The p V-diagram above represents the states of an ideal
gas during one cycle of operation of a reversible heat engine.
The cycle consists of the following four processes.
Process
Nature of Process
AB
Constant temperature ( Th = 500 K)
BC
Adiabatic
CD
Constant temperature ( Tc = 200 K)
DA
Adiabatic
During process A B, the volume of the gas increases from Vo to
2Vo and the gas absorbs 1,000 joules of heat.
a.
The pressure at A is Po. Determine the pressure at B.
b. Using the first law of thermodynamics, determine the work
performed by or on the gas during the process A B.
D. Identify the isometric processes.
E. Identify the isobaric processes.
c. During the process AB, does the entropy of the gas increase,
decrease, or remain unchanged? Justify your answer.
F. Determine the work done in the isometric processes.
d.
Calculate the heat Qc given off by the gas in the process CD.
G. Determine the work done by the gas in process 12.
H. Determine the work done on the gas in process 34.
I. Determine the net work done by the gas in one complete cycle.
J. Determine the net change in internal energy for one complete
cycle.
e. During the full cycle ABCDA is the total work the gas
performs on its surroundings positive, negative, or zero? Justify
your answer.