Physics 1501: Lecture 37 Today ’ s Agenda

1. Physics 1501: Lecture 37Today’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

2. Chap. 18: Work & 1st 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).

3. T2 T1 = 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. U2 U1 Zeroth Law of Thermodynamics • Thermal equilibrium: when objects in thermal contact cease heat transfer • same temperature B C A

4. work done “on” the system heat flow “in” (+) or “out” (-) variation of internal energy First Law of Thermodynamics • First Law of Thermodynamics U = Q + W • Independent of path in PV-diagram • Depends only on state of the system (P,V,T, …) • Energy conservation statement  only U changes

5. Heat 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 coldreservoirs*(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

6. 1 1 2 Gas Gas Gas Gas P T=TC T=TH T=TH T=TC 1 2 TH 3 4 TC V Va Vb 3 4 Heat Engines We can represent this cycle on a P-V diagram: • Example: the Stirling cycle *reservoir: large body whose temperature does not change when it absorbs or gives up heat

7. P 1 2 TH 3 4 TC V Va Vb Heat Engines • 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: 2 1 step 3 4 ADDED ADDED ADDED ADDED HEAT REMOVED REMOVED REMOVED REMOVED BY BY BY BY WORK ON ON ON ON U = Q + W

8. Realistic Stirling Engines • 2 types • Alpha-type: 2 separate chambers • beta-type: joined chambers From Wikipedia

9. Realistic Stirling Engines • 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 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. • Alpha-type • Minimum volume: gas will now expand in the hot cylinder, be heated once more, driving the hot piston in its power stroke. • 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.

10. Realistic 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.

11. Another look at beta-type • “real” one

12. P Area = Weng Chap. 19: Heat Engines and the 2nd Law 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 Qh Weng Engine Engine Qc Cold reservoir V

13. Heat Engines and the 2nd Law of Thermodynamics • A heat engine goes through a cycle • 1st Law gives U = Q + W =0 • So Qnet=|Qh| - |Qc| = -W = Weng Hot reservoir Qh Weng Engine Engine Qc Cold reservoir

14. Efficiency of a Heat Engine • How can we define a “figure of merit” for a heat engine? • Define the efficiency e as: It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work

15. Heat Engines and the Second law of Thermodynamics Reservoir It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work Qh Weng Engine Engine

16. A) eI < eII B) eI> eII C) Not enough data to determine Lecture 37: Act 1Efficiency • 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 eI, the efficiency of engine I, to eII, the efficiency of engine II.

17. Reversible/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)

18. The Carnot Engine • No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs. P • AB, the gas expands isothermally while in contact with a reservoir at Th • BC, the gas expands adiabatically (Q=0) • CD, the gas is compressed isothermally while in contact with a reservoir at Tc • DA, the gas compressed adiabatically (Q=0) A B Weng D C V

19. The Carnot Engine • Carnot showed that the thermal efficiency of a Carnot engine is: • 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.

20. Entropy and the 2nd Law • Consider a reversible process between two equilibrium states The change in entropy DS between the two states is given by the energy Qrtransferred along the reversible path divided by the absolute temperature T of the system in this interval. • The Second Law of Thermodynamics “There is a quantity known as entropy that in a closed system always remains the same (reversible) or increases (irreversible).” • Entropy is a measure of disorder in a system.

21. Entropy and the 2nd 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 all atoms no atoms