1. Heat Engines Introduction Section 0 Lecture 1 Slide 1 Lecture 25 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 25 Heat Engines and the 2 nd Law of Thermodynamics

2. Heat Engines Introduction Section 0 Lecture 1 Slide 2 Lecture 25 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Heat Engines Introduction Section 0 Lecture 1 Slide 3 Lecture 25 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 25 Heat Engines and the 2 nd Law of Thermodynamics Review of Thermodynamics

4. Heat Engines Introduction Section 0 Lecture 1 Slide 4 Lecture 25 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT -1 or m/s) Acceleration—how fast velocity is changing with time (LT -2 or m/s 2 ) Force— what is required to change to motion of a body (MLT -2 or kg-m/s 2 or N) Inertia (mass)— a measure of the force needed to change the motion of a body (M) Energy—the potential for an object to do work. (ML 2 T -2 or kg m 2 /s 2 or N-m or J) Work is equal to the force applied times the distance moved. W = F d Kinetic Energy is the energy associated with an object’s motion. KE=½ mv 2 Potential Energy is the energy associated with an objects position. Gravitational potential energy PE gravity =mgh Spring potential energy PE apring = -kx Momentum— the potential of an object to induce motion in another object (MLT -1 or kg-m/s) Angular Momentum and Rotational Energy— the equivalent constants of motion for rotation (MT -1 or kg/s) and (MLT -2 or kg m/s 2 or N) Pressure— force divided by the area over which the force is applied (ML -1 T -1 or kg/m-s or N/m 2 or Pa)

5. Heat Engines Introduction Section 0 Lecture 1 Slide 5 Lecture 25 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Dennison’s Laws Thermal Poker (or How to Get a Hot Hand in Physics) 0 th Law: Full House beats Two Pairs 1 st Law: We’re playing the same game (but with a wild card) 2 nd Law: You can’t win in Vegas. 3 rd Law: In fact, you always loose. 0 th Law: Defines Temperature 1 st Law: Conservation of Energy (with heat) 2 nd Law: You can’t recover all heat losses (or defining entropy) 3 rd Law: You can never get to absolute 0.

6. Heat Engines Introduction Section 0 Lecture 1 Slide 6 Lecture 25 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What is heat? What is the relationship between quantity of heat and temperature? What happens to a body (solid, liquid, gas) when thermal energy is added or removed? Thermal Energy Heat Solid: Atoms vibrating in all directions about their fixed equilibrium (lattice) positions. Atoms constantly colliding with each other. Liquid: Atoms still oscillating and colliding with each other but they are free to move so that the long range order (shape) of body is lost. Gas: No equilibrium position, no oscillations, atoms are free and move in perpetual high-speed “zig-zag” dance punctuated by collisions. gas liquid solid

7. Heat Engines Introduction Section 0 Lecture 1 Slide 7 Lecture 25 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 + + + + + + + + + Heat k B is Boltzmann’s constant =1.38 10 -23 J/K Solid

8. Heat Engines Introduction Section 0 Lecture 1 Slide 8 Lecture 25 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 When two objects at different temperatures are placed in contact, heat will flow from the object with the higher temperature to the object with the lower temperature. Heat added increases temperature, and heat removed decreases temperature. Heat and temperature are not the same. Temperature is a quantity that tells us which direction the heat will flow. Heat is a form of energy. (Here comes conservation of energy!!!) Temperature and Heat

9. Heat Engines Introduction Section 0 Lecture 1 Slide 9 Lecture 25 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Joule’s Experiment and the First Law of Thermodynamics Joule’s experiments led to Kelvin’s statement of the first law of thermodynamics. –Both work and heat represent transfers of energy into or out of a system. –If energy is added to a system either as work or heat, the internal energy of the system increases accordingly. The increase in the internal energy of a system is equal to the amount of heat added to a system minus the amount of work done by the system.  U = Q - W

10. Heat Engines Introduction Section 0 Lecture 1 Slide 10 Lecture 25 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Gas Behavior and The First Law Consider a gas in a cylinder with a movable piston. If the piston is pushed inward by an external force, work is done on the gas, adding energy to the system. The force exerted on the piston by the gas equals the pressure of the gas times the area of the piston: F = PA The work done equals the force exerted by the piston times the distance the piston moves: W = Fd = (PA)d = P  V

11. Heat Engines Introduction Section 0 Lecture 1 Slide 11 Lecture 25 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 25 Heat Engines and the 2 nd Law of Thermodynamics Heat Engines

12. Introduction Section 0 Lecture 1 Slide 12 Lecture 25 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Heat Engines It is a device that uses input heat to generate useful work. From the 1 st Law (Conservation of Energy) In cyclic engines we return to the original state every cycle so What is a heat engine?

13. Heat Engines Introduction Section 0 Lecture 1 Slide 13 Lecture 25 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Heat Engines All heat engines share these main features of operation: –Thermal energy (heat) is introduced into the engine. –Some of this energy is converted to mechanical work. –Some heat (waste heat) is released into the environment at a temperature lower than the input temperature. What is a heat engine?

14. Heat Engines Introduction Section 0 Lecture 1 Slide 14 Lecture 25 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Efficiency Efficiency is the ratio of the net work done by the engine to the amount of heat that must be supplied to accomplish this work. Or from the 1st Law

15. Heat Engines Introduction Section 0 Lecture 1 Slide 15 Lecture 25 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 A heat engine takes in 1200 J of heat from the high- temperature heat source in each cycle, and does 400 J of work in each cycle. What is the efficiency of this engine? a)33% b)40% c)66% Q H = 1200 J W = 400 J e = W / Q H = (400 J) / (1200 J) = 1/3 = 0.33 = 33%

16. Heat Engines Introduction Section 0 Lecture 1 Slide 16 Lecture 25 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How much heat is released into the environment in each cycle? a)33 J b)400 J c)800 J d)1200 J Q C = Q H - W = 1200 J - 400 J = 800 J

17. Heat Engines Introduction Section 0 Lecture 1 Slide 17 Lecture 25 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Carnot Engine and Carnot Cycle Carnot considered the ideal (most efficient possible) engine for a give T H and T C. Carnot engine has negligible work lost to friction, turbulence, heat loss, etc. Carnot also reasoned that the processes should occur without undue turbulence. –The engine is completely reversible: it can be turned around and run the other way at any point in the cycle, because it is always near equilibrium. –This is Carnot’s ideal engine. The cycle devised by Carnot that an ideal engine would have to follow is called a Carnot cycle. An (ideal, not real) engine following this cycle is called a Carnot engine.

18. Heat Engines Introduction Section 0 Lecture 1 Slide 18 Lecture 25 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Carnot Efficiency The efficiency of Carnot’s ideal engine (one using an ideal gas with PV=Nk B T) is called the Carnot efficiency and is given by: This is the maximum efficiency possible for any engine taking in heat from a reservoir at absolute temperature T H and releasing heat to a reservoir at temperature T C. This provides a useful limiting case. Even Carnot’s ideal engine is less than 100% efficient.

19. Heat Engines Introduction Section 0 Lecture 1 Slide 19 Lecture 25 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 1.Heat flows into cylinder at temperature T H. The fluid expands isothermally and does work on the piston. 2.The fluid continues to expand adiabatically (without heat loss). 3.Work is done by the piston on the fluid, which undergoes an isothermal compression. 4.The fluid returns to its initial condition by an adiabatic compression. Carnot Cycle

20. Heat Engines Introduction Section 0 Lecture 1 Slide 20 Lecture 25 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 A steam turbine takes in steam at a temperature of 400  C and releases steam to the condenser at a temperature of 120  C. What is the Carnot efficiency for this engine? a)30% b)41.6% c)58.4% d)70% T H = 400  C = 673 K T C = 120  C = 393 K e C = (T H - T C ) / T H = (673 K - 393 K) / (673 K) = 280 K / 673 K = 0.416 = 41.6%

21. Heat Engines Introduction Section 0 Lecture 1 Slide 21 Lecture 25 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 If the turbine takes in 500 kJ of heat in each cycle, what is the maximum amount of work that could be generated by the turbine in each cycle? a)0.83 J b)16.64 kJ c)28 kJ d)208 kJ Q H = 500 kJ e = W / Q H, so W = e Q H = (0.416)(500 kJ) = 208 kJ

22. Heat Engines Introduction Section 0 Lecture 1 Slide 22 Lecture 25 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 25 Heat Engines and the 2 nd Law of Thermodynamics Second Law of Thermodynamics

23. Heat Engines Introduction Section 0 Lecture 1 Slide 23 Lecture 25 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Second Law of Thermodynamics You can’t recover all heat losses. You can’t win in Vegas. No engine, working in a continuous cycle, can take heat from a reservoir at a single temperature and convert that heat completely to work. Therefore, no engine can have a greater efficiency than a Carnot engine operating between the same two temperatures. Define entropy (something that measures randomness or disorder in an object) to take account of this. Heat (random motion) is a special form of energy that cannot be fully (with complete efficiency) transformed to other forms of energy. This leads to various forms of the Second Law of Thermodynamics.

24. Heat Engines Introduction Section 0 Lecture 1 Slide 24 Lecture 25 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Second Law of Thermodynamics An engine with an efficiency greater than the Carnot engine would produce a greater amount of work than the Carnot engine, for the same amount of heat input Q H. Some of this work could be used to run the Carnot engine in reverse, returning the heat released by the first engine to the higher- temperature reservoir.

25. Heat Engines Introduction Section 0 Lecture 1 Slide 25 Lecture 25 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Second Law of Thermodynamics The remaining work W excess would be available for external use, and no heat would end up in the lower-temperature reservoir. The two engines would take a small quantity of heat from the higher-temperature reservoir and convert it completely to work. This would violate the second law of thermodynamics.

26. Heat Engines Introduction Section 0 Lecture 1 Slide 26 Lecture 25 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology Next Lab/Demo: Fluid Dynamics Temperature Thursday 1:30-2:45 ESLC 46 Ch 9 and 10 Next Class: Wednesday 10:30-11:20 BUS 318 room Review Ch 10