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Work

Work. Thermodynamics Professor Lee Carkner Lecture 7. PAL # 6 Equations of State. CO 2 flow through a pipe From Table A-1: R = 0.1889 kPa m 3 / kg K T cr = 304.2 K, P cr = 7.39 MPa V’ 1 = (2)(0.1889)(500) / 3000 = 0.06297 m 3 /s V’ 2 = (2)(0.1889)(450) / 3000 = 0.05667 m 3 /s

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  1. Work Thermodynamics Professor Lee Carkner Lecture 7

  2. PAL # 6 Equations of State • CO2 flow through a pipe • From Table A-1: • R = 0.1889 kPa m3 / kg K • Tcr = 304.2 K, Pcr = 7.39 MPa • V’1 = (2)(0.1889)(500) / 3000 = 0.06297 m3/s • V’2 = (2)(0.1889)(450) / 3000 = 0.05667 m3/s • r1 = m’/V’ = 2/0.6297 = • r2 = 2/0.05667 =

  3. PAL # 6 Equations of State • Use PR and TR to find Z from chart A-15 • PR = P/Pcr = 3/7.39 =0.407 • TR1 =500/304.2 = • TR2 = 450/304.2 = • V’1 = (0.9791)(0.06297) = 0.06165 • 2.1% error • r1 =32.44, error =2.1 % • V’2 =(0.9656)(0.05667) = 0.05472 • 3.6% error • r2 = 36.55, error =3.6 %

  4. Exam #1 • Friday, March 24th • Covers: • Lectures 1-8 • Chapters 1-4 • Format: • About 10 multiple choice (~25% weight) • About 4 problems (~75%weight) • Equations provided • Bring just pencil and calculator • Worth 15% of final grade

  5. Work • No displacement, No work • We consider now external work • Involves interaction with another system or its surroundings (external to the system) • Work is a form of energy

  6. Work and Hydrostatic Systems • Work is not a property of the system • We need to be able to specify the properties of the system at each point in the process • Called a quasi-equilibrium or quasi-static process

  7. Derivation of Work

  8. Work, Pressure and Volume dW = F ds dW = P dV • If dV is positive (increase in V) then W is positive (work by the system)

  9. Total Work W =  P dV • Need to know P as a function of V • Often need to limit or parameterize T • W depends on both the change of volume and how the volume changed

  10. PV Diagram • The process by which the volume changes is a line or curve connecting the two points • For different processes, different curves, different amounts of work

  11. Path Dependence of Work

  12. Path Dependence • What are the paths? • follow isotherm • horizontal • vertical

  13. Closed Cycle • If the system moves from 1 to 2 and then back to 1, it is a cycle • if two different paths are traveled W is the area between the curves • Repeat the same process over and over, extract work each cycle

  14. Cycle Work

  15. Polytropic Process • Often for compression and expansion of a gas, pressure and volume are related by: • Where C and n are constants • Called a polytropic process • Can integrate between points 1 and 2: • For an ideal gas, can replace PV with mRT

  16. Polytrope

  17. Isothermal Process W =  C(1/V) dV = PV ln (V2/V1) • For an ideal gas PV = mRT so PV is constant

  18. Piston of Air

  19. Energy Balance Qnet,in – Wnet,out =DEsystem Q – W = DE • First Law of Thermodynamics • We make a distinction between Q and W for eventual use with the second law

  20. Specific Heat • The temperature change due to the energy change can be found with two specific quantities: • Specific heat at constant volume • Specific heat at constant pressure • Units of kJ/kg K

  21. cv and cP

  22. Specific Energy • As energy is added to a system the rate of temperature change changes • c tells you the energy needed to effect a change

  23. Temperature Dependence of c

  24. Next Time • Read: 4.4-4.5 • Homework: Ch 4, P: 36, 56, 74 • Test 1 Friday

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