about first law of thermodynamics

1. PHYSICS 231
INTRODUCTORY PHYSICS I
Lecture 18

2. The Laws of ThermodynamicsThe Laws of Thermodynamics
Chapter 12

3. Principles of Thermodynamics
• Energy is conserved
• FIRST LAW OF THERMODYNAMICS
• Examples:
• Engines (Heat -> Mechanical Energy)
• Friction (Mechanical Energy -> Heat)
• All processes must increase entropy
• SECOND LAW OF THERMODYNAMICS
• Entropy is measure of disorder
• Engines can not be 100% efficient

4. • Adding heat Q can:
• Change temperature
• Change state of matter
• Can also change ∆U by doing work on the gas
Work done on a gas
Change of
Internal Energy ∆U
Work done on the gas
W=
r
F⋅∆
r
x=F(−∆y)=(PA)(−∆y)
W=−P∆V

5. First Law of Thermodynamics
∆U=Q+W
Note:
(Work done by the gas) = - (Work done on the gas)
•Conservation of Energy
•Can change internal energy ∆U by
• Adding heat to gas: Q
• Doing work on gas: W=−P∆V
Q=∆U+Wbythegas
Add heat => Increase Int. Energy & Gas does work
Wbythegas=+P∆V

6. Example 12.1
A cylinder of radius 5 cm is kept at pressure with a
piston of mass 75 kg.
a) What is the pressure inside the cylinder?
b) If the gas expands such that the
cylinder rises 12.0 cm, what work was
done by the gas?
c) What amount of the work went into
changing the gravitational PE of the
piston?
d) Where did the rest of the work go?
1.950x105
Pa
183.8 J
88.3 J
Compressing the outside air

7. Example 12.2a
A massive copper piston traps an ideal
gas as shown to the right. The piston is
allowed to freely slide up and down and
equilibrate with the outside air.
The pressure inside the
cylinder is _________ the
pressure outside.
a) Greater than
b) Less than
c) Equal to

8. Example 12.2b
A massive copper piston traps an ideal
gas as shown to the right. The piston is
allowed to freely slide up and down and
equilibrate with the outside air.
The temperature inside the cylinder
is __________ the temperature
outside.
a) Greater than
b) Less than
c) Equal to

9. Example 12.2c
A massive copper piston traps an ideal
gas as shown to the right. The piston
is allowed to freely slide up and down
and equilibrate with the outside air.
If the gas is heated by a steady
flame, and the piston rises to a new
equilibrium position, the new pressure
will be _________ than
the previous pressure.
a) Greater than
b) Less than
c) Equal to

10. Some Vocabulary
• Isobaric
• P = constant
• Isovolumetric
• V = constant
• W = 0
• Isothermal
• T = constant
• ∆U = 0 (ideal gas)
• Adiabatic
• Q = 0
V
V
V
V
P
P
P
P

11. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
isothermally compressing the gas to
half its original volume (b)
Pb is _______ Pa
Outside Air: Room T, Atm. PExample 12.3a
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

12. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
isothermally compressing the gas to
half its original volume (b)
Tb is ________ Ta
Outside Air: Room T, Atm. PExample 12.3b
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

13. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
isothermally compressing the gas to
half its original volume (b)
Wab is ________ 0
Outside Air: Room T, Atm. P
Vocabulary: Wab is work done by gas between a and b
Example 12.3c
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

14. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
isothermally compressing the gas to
half its original volume (b)
Ub is ________ Ua
Outside Air: Room T, Atm. PExample 12.3d
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

15. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
isothermally compressing the gas to
half its original volume (b)
Qab is ________ 0
Outside Air: Room T, Atm. P
Vocabulary: Qab is heat added to gas between a and b
Example 12.3e
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

16. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
adiabatically compressing the gas to
half its original volume (b)
Pb is _______ Pa
Outside Air: Room T, Atm. PExample 12.4a
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

17. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
adiabatically compressing the gas to
half its original volume (b)
Wab is ______ 0
Outside Air: Room T, Atm. PExample 12.4b
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

18. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
adiabatically compressing the gas to
half its original volume (b)
Qab is _______ 0
Outside Air: Room T, Atm. PExample 12.4c
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

19. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
adiabatically compressing the gas to
half its original volume (b)
Ub is _______ Ua
Outside Air: Room T, Atm. PExample 12.4d
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

20. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
Weight is slowly added to the piston,
adiabatically compressing the gas to
half its original volume (b)
Tb is _______ Ta
Outside Air: Room T, Atm. PExample 12.4e
a) Greater than
b) Less than
c) Equal to
∆U=Q−P∆V
Wbythegas =P∆V

21. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
The gas is cooled, isobarically
compressing the gas to half its
original volume (b)
Pb is _______ Pa
Outside Air: Room T, Atm. PExample 12.5a
a) Greater than
b) Less than
c) Equal to
PV = nRT
∆U=Q−P∆V
Wbythegas =P∆V

22. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
The gas is cooled, isobarically
compressing the gas to half its
original volume (b)
Wab is _______ 0
Outside Air: Room T, Atm. PExample 12.5b
a) Greater than
b) Less than
c) Equal to
PV = nRT
∆U=Q−P∆V
Wbythegas =P∆V

23. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
The gas is cooled, isobarically
compressing the gas to half its
original volume (b)
Tb is _______ Ta
Outside Air: Room T, Atm. PExample 12.5c
a) Greater than
b) Less than
c) Equal to
PV = nRT
∆U=Q−P∆V
Wbythegas =P∆V

24. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
The gas is cooled, isobarically
compressing the gas to half its
original volume (b)
Ub is _______ Ua
Outside Air: Room T, Atm. PExample 12.5d
a) Greater than
b) Less than
c) Equal to
PV = nRT
∆U=Q−P∆V
Wbythegas =P∆V

25. A massive piston traps an amount of
Helium gas as shown. The piston freely
slides up and down.
The system initially equilibrates at
room temperature (a)
The gas is cooled, isobarically
compressing the gas to half its
original volume (b)
Qab is _______ 0
Outside Air: Room T, Atm. PExample 12.5e
a) Greater than
b) Less than
c) Equal to
PV = nRT
∆U=Q−P∆V
Wbythegas =P∆V

26. P-V Diagrams
P
V
Path moves to right:
Wby the gas = Area under curve
P
V
Path moves to left:
Wby the gas = - Area under curve
(Won the gas = - Wby the gas)

27. Work from closed cycles
Consider cycle A -> B -> A
WA->B = Area
WB->A = - Area
(work done by gas)

28. Work from closed cycles
Consider cycle A -> B -> A
WA->B->A= Area
(work done by gas)

29. Work from closed cycles
Reverse the cycle, make it counter clockwise
WB->A = - Area
WA->B = Area
(work done by gas)

30. Work from closed cycles
WA->B->A= - Area
Reverse the cycle, make it counter clockwise
(work done by gas)

31. Internal Energy in closed cycles
in closed cycles∆U=0

32. Example 12.6 a) What amount of work is
performed by the gas in the
cycle IAFI?
b) How much heat was
inserted into the gas in the
cycle IAFI?
c) What amount of work is
performed by the gas in the
cycle IBFI?
W=3.04x105
J
W = -3.04x105
J
Q = 3.04x105
J
V (m3
)

33. Example 12.7Consider a monotonic ideal gas.
a) What work was done by
the gas from A to B?
b) What heat was added to
the gas between A and B?
c) What work was done by
the gas from B to C?
d) What heat was added to
the gas beween B and C?
e) What work was done by
the gas from C to A?
f) What heat was added to
the gas from C to A?
V (m3
)
P (kPa)
25
50
75
0.2 0.4 0.6
A
B
C
20,000 J
20,000
-10,000 J
-25,000 J
0
15,000 J

34. Example Continued
Take solutions from last problem and find:
a) Net work done by gas in the cycle
b) Amount of heat added to gas
WAB + WBC + WCA = 10,000 J
QAB + QBC + QCA = 10,000 J
This does NOT mean that the engine is 100% efficient!

35. Example 12.8a
Consider an ideal gas
undergoing the trajectory
through the PV diagram.
In going from A to B to
C, the work done BY the
gas is _______ 0.
P
V
A
B
a) >
b) <
c) =
C

36. Example 12.8b
In going from A to B to
C, the change of the
internal energy of the
gas is _______ 0.
P
V
A
B
a) >
b) <
c) =
C

37. Example 12.8c
In going from A to B to
C, the amount of heat
added to the gas is
_______ 0.
P
V
A
B
a) >
b) <
c) =
C
D

38. Example 12.8d
In going from A to B to
C to D to A, the work
done BY the gas is
_______ 0.
P
V
A
B
a) >
b) <
c) =
C
D

39. Example 12.8e
In going from A to B to
C to D to A, the change
of the internal energy of
the gas is _______ 0.
P
V
A
B
a) >
b) <
c) =
C
D

40. Example 12.8f
In going from A to B to
C to D to A, the heat
added to the gas is
_______ 0.
P
V
A
B
a) >
b) <
c) =
C
D