11/19/2013PHY 113 C Fall Lecture 231 PHY 113 C General Physics I 11 AM – 12:15 PM MWF Olin 101 Plan for Lecture 23: Chapter 22: Heat engines 1.Thermodynamic cycles; work and heat efficiency 2.Carnot cycle 3.Otto cycle; diesel cycle 4.Brief comments on entropy

11/19/2013 PHY 113 C Fall Lecture 232

11/19/2013PHY 113 C Fall Lecture 233 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

11/19/2013PHY 113 C Fall Lecture 234 Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matter

11/19/2013PHY 113 C Fall Lecture 235 Webassign – Assignment 20 The rms speed of an oxygen molecule (O 2 ) in a container of oxygen gas is 563 m/s. What is the temperature of the gas?

11/19/2013PHY 113 C Fall Lecture 236 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.  E int = Q + 0 = 213J + 0 = 213 J

11/19/2013PHY 113 C Fall Lecture 237 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. (a)What is the final pressure of the gas? (b)What are the initial and final temperatures? (c)Find Q for the gas during this process. (d)Find ΔE int for the gas during this process. (e)Find W for the gas during this process.

11/19/2013PHY 113 C Fall Lecture 238 Digression: Adiabatic process (Q=0)

11/19/2013PHY 113 C Fall Lecture 239 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. (a)What is the final pressure of the gas? b)What are the initial and final temperatures? PV=nRT c)Find Q for the gas during this process. Q=0 d)Find ΔE int for the gas during this process. ΔE int =W e)Find W for the gas during this process. For diatomic ideal gas: 

11/19/2013PHY 113 C Fall Lecture 2310 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)?

11/19/2013PHY 113 C Fall Lecture 2311 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?

11/19/2013PHY 113 C Fall Lecture 2312 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 

11/19/2013PHY 113 C Fall Lecture 2313 Thermodynamic cycles for designing ideal engines and heat pumps P (1.013 x 10 5 ) Pa ViVi VfVf PiPi PfPf A BC D Engine process:

11/19/2013PHY 113 C Fall Lecture 2314 P (1.013 x 10 5 ) Pa ViVi VfVf PiPi PfPf A BC D Examples process by an ideal gas: ABABBCBCCDCDDADA Q W0-P f (V f -V i )0P i (V f -V i )  E int

11/19/2013PHY 113 C Fall Lecture 2315 Example from homework

11/19/2013PHY 113 C Fall Lecture 2316 Most efficient thermodynamic cycle -- Carnot Sadi Carnot

11/19/2013PHY 113 C Fall Lecture 2317 Carnot cycle: A  B Isothermal at T h B  C Adiabatic C  D Isothermal at T c D  A Adiabatic

11/19/2013PHY 113 C Fall Lecture 2318 iclicker exercise: We discussed the efficiency of an engine as Is this result A.Special to the Carnot cycle B.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 A.Special to the Carnot cycle B.General to all ideal thermodynamic cycles

11/19/2013PHY 113 C Fall Lecture 2319 For Carnot cycle:

11/19/2013PHY 113 C Fall Lecture 2320 iclicker exercise: Why should we care about the Carnot cycle? A.We shouldn’t B.It approximately models some heating and cooling technologies C.It provides insight into another thermodynamic variable -- entropy

11/19/2013PHY 113 C Fall Lecture 2321

11/19/2013PHY 113 C Fall Lecture 2322 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?

11/19/2013PHY 113 C Fall Lecture 2323 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 x10 3 J of energy from the hot reservoir during the isothermal expansion. (a)Find the energy expelled to the cold reservoir in each cycle. (b)(b) Find the net work done by the gas in each cycle.

11/19/2013PHY 113 C Fall Lecture 2324 The Otto cycle V 1 /V 2 is the “compression ratio” -- typically V 1 /V 2 = 8   =0.56

11/19/2013PHY 113 C Fall Lecture 2325

11/19/2013PHY 113 C Fall Lecture 2326 The Diesel cycle In principle, higher efficiency than comparable Otto cycle.

11/19/2013PHY 113 C Fall Lecture 2327 Engine vs heating/cooling designs

11/19/2013PHY 113 C Fall Lecture 2328 Brief comments about entropy – macroscopic picture Carnot cycle

11/19/2013PHY 113 C Fall Lecture 2329 Brief comments about entropy – continued