Physics 1501: Lecture 37, Pg 1
Physics 1501: Lecture 37Physics 1501: Lecture 37TodayToday’’s Agendas Agenda
AnnouncementsHomework #12 (Dec. 9): 2 lowest droppedMidterm 2 … in class WednesdayFriday: review session … bring your questions
Today’s topicsChap.18: Heat and Work
» Zeroth Law of thermodynamics» First Law of thermodynamics and applications» Work and heat engines
Chap.19: Second law of thermodynamics» Efficiency» Entropy
Physics 1501: Lecture 37, Pg 2
Chap. 18: Work & 1Chap. 18: Work & 1stst Law Law
The Laws of Thermodynamics
0) If two objects are in thermal equilibrium with a third, they are in equilibrium with each other.
1) There is a quantity known as internal energy that in an isolated system always remains the same.
2) There is a quantity known as entropy that in a closed system always remains the same (reversible) or increases (irreversible).
Physics 1501: Lecture 37, Pg 3
Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics
Thermal equilibrium: when objects in thermal contact cease heat transfersame temperature
T1T2
U1 U2
=
If objects A and B are separately in thermal equilibrium with a third object C, then objects A and B are in
thermal equilibrium with each other.
AC
B
Physics 1501: Lecture 37, Pg 4
First Law of ThermodynamicsFirst Law of Thermodynamics First Law of Thermodynamics
U = Q + W
variation of internal energyheat flow “in” (+) or “out” (-)
work done “on” the system
Independent of path in PV-diagramDepends only on state of the system (P,V,T, …)Energy conservation statement only U changes
Physics 1501: Lecture 37, Pg 5
Heat EnginesHeat Engines We now try to do more than just raise the temperature of an
object by adding heat. We want to add heat to get some work done!
Heat engines: Purpose: Convert heat into work using a cyclic process Example: Cycle a piston of gas between hot and cold reservoirs* (Stirling cycle)
1) hold volume fixed, raise temperature by adding heat
2) hold temperature fixed, do work by expansion
3) hold volume fixed, lower temperature by draining heat
4) hold temperature fixed, compress back to original V
Physics 1501: Lecture 37, Pg 6
Heat EnginesHeat Engines Example: the Stirling cycle
GasT=TH
GasT=TH
GasT=TC
GasT=TC
V
P
TC
TH
Va Vb
1 2
34
We can represent this cycle on a P-V diagram:
11 2
34*reservoir: large body whose temperature does not change when it absorbs or gives up heat
Physics 1501: Lecture 37, Pg 7
Identify whether Heat is ADDED or REMOVED from the
gas Work is done BY or ON the gas for each
step of the Stirling cycle:
V
P
TC
TH
Va Vb
1 2
34
ADDEDREMOVED
BYON
1
HEAT
WORK
step
ADDEDREMOVED
BYON
2
ADDEDREMOVED
BYON
3
ADDEDREMOVED
BYON
4
Heat EnginesHeat Engines
U = Q + W
Physics 1501: Lecture 37, Pg 8
Realistic Stirling EnginesRealistic Stirling Engines
beta-type: joined chambers
From Wikipedia
2 typesAlpha-type: 2 separate chambers
Physics 1501: Lecture 37, Pg 9
Realistic Stirling EnginesRealistic Stirling Engines Alpha-type Most of the working gas is
in contact with the hot cylinder walls, it has been heated and expansion has pushed the hot piston to the bottom of its travel in the cylinder. The expansion continues in the cold cylinder, which is 90° behind the hot piston.
Maximum volume: the hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops.
Most pf the gas is in the cold cylinder and cooling continues. The cold piston, powered by flywheel momentum compresses the remaining part of the gas.
Minimum volume: gas will now expand in the hot cylinder, be heated once more, driving the hot piston in its power stroke.
Physics 1501: Lecture 37, Pg 10
Realistic Stirling EnginesRealistic Stirling Engines Beta-type:
Power piston (dark grey) has compressed the gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger.
The heated gas increases in pressure and pushes the power piston to the farthest limit of the power stroke.
The displacer piston now moves, shunting the gas to the cold end of the cylinder.
The cooled gas is now compressed by the flywheel momentum. This takes less energy, since when it is cooled its pressure drops.
Physics 1501: Lecture 37, Pg 11
Another look at beta-typeAnother look at beta-type
“real” one
Physics 1501: Lecture 37, Pg 12
Chap. 19: Heat Engines and the 2Chap. 19: Heat Engines and the 2ndnd Law of ThermodynamicsLaw of Thermodynamics
A schematic representation of a heat engine. The engine receives energy Qh from the hot reservoir, expels energy Qc to the cold reservoir, and does work W.
If working substance is a gas
Hot reservoir
Cold reservoir
Engine
Qh
Qc
Weng
V
P
Area = Weng
Engine
Physics 1501: Lecture 37, Pg 13
Heat Engines and the 2Heat Engines and the 2ndnd Law of Law of ThermodynamicsThermodynamics
A heat engine goes through a cycle1st Law gives
U = Q + W =0
So Qnet=|Qh| - |Qc| = -W = Weng
Hot reservoir
Cold reservoir
Engine
Qh
Qc
Weng
Engine
Physics 1501: Lecture 37, Pg 14
Efficiency of a Heat EngineEfficiency of a Heat Engine
How can we define a “figure of merit” for a heat engine? Define the efficiency as:
It is It is impossibleimpossible to construct a heat engine that, operating to construct a heat engine that, operating in a cycle, produces no other effect than the absorption in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an of energy from a reservoir and the performance of an equal amount of workequal amount of work
Physics 1501: Lecture 37, Pg 15
Heat Engines and the Second law of Heat Engines and the Second law of ThermodynamicsThermodynamics
Reservoir
Engine
Qh Weng
It is It is impossibleimpossible to to construct a heat engine construct a heat engine that, operating in a cycle, that, operating in a cycle, produces no other effect produces no other effect than the absorption of than the absorption of energy from a reservoir energy from a reservoir and the performance of and the performance of an equal amount of workan equal amount of work
Engine
Physics 1501: Lecture 37, Pg 16
Consider two heat engines: Engine I:
» Requires Qin = 100 J of heat added to system to get W=10 J of work
Engine II:
» To get W=10 J of work, Qout = 100 J of heat is exhausted to the environment
Compare I, the efficiency of engine I, to II, the efficiency of engine II.
A) I < II B) I > II C) Not enough data to determine
Lecture 37: Act 1Lecture 37: Act 1EfficiencyEfficiency
Physics 1501: Lecture 37, Pg 17
Reversible/irreversible processesReversible/irreversible processes
Reversible process: Every state along some path is an equilibrium state The system can be returned to its initial conditions along the
same path Irreversible process;
Process which is not reversible !
Most real physical processes are irreversible E.g., energy is lost through friction and the initial conditions
cannot be reached along the same path However, some processes are almost reversible
» If they occur slowly enough (so that system is almost in equilibrium)
Physics 1501: Lecture 37, Pg 18
The Carnot EngineThe Carnot Engine
No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.
A.A. AAB, the gas expands isothermally B, the gas expands isothermally while in contact with a reservoir at Twhile in contact with a reservoir at Thh
B.B. BBC, the gas expands adiabatically C, the gas expands adiabatically (Q=0)(Q=0)
C.C. CCD, the gas is compressed D, the gas is compressed isothermally while in contact with a isothermally while in contact with a reservoir at Treservoir at Tcc
D.D. DDA, the gas compressed A, the gas compressed adiabatically (Q=0)adiabatically (Q=0)
V
P
AB
CD
Weng
Physics 1501: Lecture 37, Pg 19
The Carnot EngineThe Carnot Engine
All real engines are less efficient than the Carnot engine because they operate irreversibly due to friction as they complete a cycle in a brief time period.
Carnot showed that the thermal efficiency of a Carnot Carnot showed that the thermal efficiency of a Carnot engine is:engine is:
Physics 1501: Lecture 37, Pg 20
Entropy and the 2Entropy and the 2ndnd Law Law
Consider a reversible process between two equilibrium states The change in entropy S between the two states is given by the energy Qr transferred along the reversible path divided by the absolute temperature T of the system in this interval.
The Second Law of ThermodynamicsThe Second Law of Thermodynamics
““There is a quantity known as There is a quantity known as entropyentropy that in a closed system that in a closed system always remains the same (always remains the same (reversiblereversible) or increases ) or increases ((irreversibleirreversible).).””
Entropy is a measure of disorder in a system.Entropy is a measure of disorder in a system.
Physics 1501: Lecture 37, Pg 21
Entropy and the 2Entropy and the 2ndnd Law Law What about the following situation
Atoms all located in half the room
Although possible, it is quite improbable
Disorderly arrangements are much more probable than orderly ones
Isolated systems tend toward greater disorder Entropy is a measure of that
disorder Entropy increases in all natural
processes
no atomsall atoms
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