PHY 113 C General Physics I 11 AM – 12:15 P M MWF Olin 101 Plan for Lecture 23:

1. PHY 113 C General Physics I 11 AM – 12:15 PM MWF Olin 101 Plan for Lecture 23: Chapter 22: Heat engines Thermodynamic cycles; work and heat efficiency Carnot cycle Otto cycle; diesel cycle Brief comments on entropy PHY 113 C Fall 2013 -- Lecture 23

2. PHY 113 C Fall 2013 -- Lecture 23

3. Comment about Exam 3: • Part I – take home portion (1 problem): available Thursday 11/21/2013 after class; must be turned in before Part II – in-class portion (3 problems): Tuesday 11/25/2013 • Some special arrangements for early exams have been (or will be) arranged by prior agreement • Of course, all sections of the exam are to be taken under the guidelines of the honor code PHY 113 C Fall 2013 -- Lecture 23

4. Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matter PHY 113 C Fall 2013 -- Lecture 23

5. Webassign – Assignment 20 • The rms speed of an oxygen molecule (O2) in a container of oxygen gas is 563 m/s. What is the temperature of the gas? PHY 113 C Fall 2013 -- Lecture 23

6. Webassign – Assignment 20 • In a constant-volume process, 213 J of energy is transferred by heat to 0.99 mol of an ideal monatomic gas initially at 299 K. • (a) Find the work done on the gas.(b) Find the increase in internal energy of the gas. • (c) Find its final temperature. For constant volume process, W=0. DEint= Q + 0 = 213J + 0 = 213 J PHY 113 C Fall 2013 -- Lecture 23

7. Webassign – Assignment 20 • A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.06 atm and a volume of 12.2 L to a final volume of 29.6 L. • What is the final pressure of the gas? • What are the initial and final temperatures? • Find Q for the gas during this process. • Find ΔEint for the gas during this process. • Find W for the gas during this process. PHY 113 C Fall 2013 -- Lecture 23

8. Digression: Adiabatic process (Q=0) PHY 113 C Fall 2013 -- Lecture 23

9. Webassign – Assignment 20 • A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.06 atm and a volume of 12.2 L to a final volume of 29.6 L. • What is the final pressure of the gas? • What are the initial and final temperatures? • PV=nRT • Find Q for the gas during this process. Q=0 • Find ΔEint for the gas during this process. ΔEint=W • Find W for the gas during this process. For diatomic ideal gas: g = 1.4 PHY 113 C Fall 2013 -- Lecture 23

10. Webassign – Assignment 20 • (a) How much work is required to compress 4.95 mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an isothermal process?(b) How much work is required to produce the same compression in an adiabatic process?(c) What is the final pressure in part (a)?(d) What is the final pressure in part (b)? PHY 113 C Fall 2013 -- Lecture 23

11. Webassign – Assignment 20 • (a) How much work is required to compress 4.95 mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an isothermal process? PHY 113 C Fall 2013 -- Lecture 23

12. Webassign – Assignment 20 • (b) How much work is required to compress 4.95 mol of air at 19.6°C and 1.00 atm to one-tenth of the original volume by an adiabatic process? Note: assume g=1.4 PHY 113 C Fall 2013 -- Lecture 23

13. Pf B C P (1.013 x 105) Pa A D Pi Vi Vf Thermodynamic cycles for designing ideal engines and heat pumps http://auto.howstuffworks.com/engine1.htm Engine process: PHY 113 C Fall 2013 -- Lecture 23

14. Pf B C P (1.013 x 105) Pa A D Pi Vi Vf Examples process by an ideal gas: PHY 113 C Fall 2013 -- Lecture 23

15. Example from homework PHY 113 C Fall 2013 -- Lecture 23

16. Most efficient thermodynamic cycle -- Carnot Sadi Carnot 1796-1832 PHY 113 C Fall 2013 -- Lecture 23

17. Carnot cycle: AB Isothermal at Th BC Adiabatic CD Isothermal at Tc DA Adiabatic PHY 113 C Fall 2013 -- Lecture 23

18. iclicker exercise: • We discussed the efficiency of an engine as • Is this result • Special to the Carnot cycle • General to all ideal thermodynamic cycles • iclicker exercise: • We discussed the efficiency of an engine running with hot and cold reservoirs as • Is this result • Special to the Carnot cycle • General to all ideal thermodynamic cycles PHY 113 C Fall 2013 -- Lecture 23

19. For Carnot cycle: PHY 113 C Fall 2013 -- Lecture 23

20. iclicker exercise: • Why should we care about the Carnot cycle? • We shouldn’t • It approximately models some heating and cooling technologies • It provides insight into another thermodynamic variable -- entropy PHY 113 C Fall 2013 -- Lecture 23

21. PHY 113 C Fall 2013 -- Lecture 23

22. Webassign Assignment 21 • A heat engine operates between a reservoir at 28°C and one at 362°C. What is the maximum efficiency possible for this engine? PHY 113 C Fall 2013 -- Lecture 23

23. Webassign Assignment 21 • An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 260°C, and the isothermal compression takes place at 50.0°C. The gas takes in 1.28 x103J of energy from the hot reservoir during the isothermal expansion. • Find the energy expelled to the cold reservoir in each cycle. • (b) Find the net work done by the gas in each cycle. PHY 113 C Fall 2013 -- Lecture 23

24. The Otto cycle V1/V2 is the “compression ratio” -- typically V1/V2= 8 e=0.56 PHY 113 C Fall 2013 -- Lecture 23

25. PHY 113 C Fall 2013 -- Lecture 23

26. The Diesel cycle In principle, higher efficiency than comparable Otto cycle. PHY 113 C Fall 2013 -- Lecture 23

27. Engine vs heating/cooling designs PHY 113 C Fall 2013 -- Lecture 23

28. Brief comments about entropy – macroscopic picture Carnot cycle PHY 113 C Fall 2013 -- Lecture 23

29. Brief comments about entropy – continued PHY 113 C Fall 2013 -- Lecture 23