Physics 1501: Lecture 37, Pg 1 Physics 1501: Lecture 37 Physics 1501: Lecture 37 Today Today ’ ’ s Agenda s Agenda Announcements Homework #12 (Dec. 9): 2 lowest dropped Midterm 2 … in class Wednesday Friday: review session … bring your questions Today’s topics Chap.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
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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.
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
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