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Review

Review. System Property State Process Cycle Zeroth Law. Example 2-4. Applied Thermodynamics. Thermodynamics: Energy, Work, Power and Heat. Energy. Forms of Energy Kinetic: KE = ½ mv 2 Potential: PE = mgh Specific energy: ke = ½ v 2 pe = gh Internal energy, U Efficiency, η.

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Review

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  1. Review • System • Property • State • Process • Cycle • Zeroth Law

  2. Example 2-4

  3. Applied Thermodynamics Thermodynamics: Energy, Work, Power and Heat

  4. Energy • Forms of Energy • Kinetic: KE = ½ mv2 • Potential: PE = mgh • Specific energy: • ke = ½ v2 • pe = gh • Internal energy, U • Efficiency, η

  5. Energy • Total ∆Esystem has three macroscopic quantities: • ∆KE: motion of system • ∆PE: displacement of system in a gravitational field • ∆U: Internal Energy is an extensive property.

  6. Energy: Forms or Carriers • Many forms: kinetic, potential, thermal, radiant, elastic, chemical etc…. • Energy is [ex]changed (dynamic) and stored (static) • It may be better to say energy is carried.

  7. Work: Definition • Means of energy transfer across a boundary: • Expansion workWk = ΣF δx = F ∆x = F (x2 – x1) Wk = Σp A δx = = Σp δV= p ∆V • Shaft WorkWk = Σ Tδθ= T ∆ θ =T (θ2 – θ1) 1 1 P P 2 2 dV dV V V

  8. Work: Sign Convention • W>0: work transfer out of system • W<0: work transfer into system

  9. Caution! Work ispath dependent • dW = p∙dV ----- meaningless because: ∫dW = W2 – W1 = ∫p ∙ dV Implies we can assign values to W1 and W2 . • Instead we write δW = p ∙ dV and W = ∫δW = ∫p ∙ dV Where δW is an inexactdifferential.i.e. the left side cannot be integrated and evaluated at the limits. • Work is not a property.

  10. Example: Work • CO2 is slowly heated from 50C to 500C in two steps as shown. • p1 = 100 kPa • p3 = 150 kPa • T2 = 350C • m= 0.044kg • Calculate total Work. P 2 3 P2=P3 1 P1 V V1 V2 V3

  11. Example: Work • Assume quasi-equilibrium • Assume Ideal gas P 2 3 P2=P3 1 P1 V V1 V2 V3

  12. Power • Energy flow or energy current Power = dE/dt = IE • Rate of doing Work Power = dW/dt = F∙ dx/dt = F ∙ v W = ∫F ∙ v dt =∫p ∙ dV • Involves a flow across a potential Power = -Δp |dV/dt| = -Δφ |dq/dt| = V∙Iq

  13. Heat: Definition • Thermal energy moving across a boundary (not the lay definition) • Only induced by a temperature difference • Adiabatic process: no transfer of heat • Like work, heat depends on the process, • Heat is not a property • Q>0: heat transfer to system • Q<0: heat transfer from the system

  14. Equivalence of Work and Heat • Heat and work are both energy transitions • Work can affect a system as if heat had been transferred. (the opposite is not always true)

  15. Internal Energy • In a Macroscopic analysis anything not KE or PE is Internal Energy, U. • Specific internal energy, u = U/m, is intensive. • Sensible U – related to temperature • Latent U – associated with phase change • Microscopically Internal Energy is made of: • Translation, Rotation and Vibration of molecules • Chemical bonds within molecules • Plus: orbital states, nuclear spin and nuclear forces

  16. Work in a Polytropic Process • pVn = constant • If n≠1, general polytropic process • If n = 1, isothermal process • If n = 0, isobaric process

  17. 1 3.0 2c p (bar) 2b pVn=k 2a 0.1 0.2 V (m3) Example: Polytropic Process • A gas in a piston–cylinder assembly undergoes a process for which: pVn = constant Pi= 3 bar, Vi= 0.1 m3, Vf= 0.2 m3 • Determine the Work if a) n=1.5, b) n=1.0, c) n=0

  18. 1 3.0 p (bar) pVn=k 2a 0.1 0.2 V (m3) Example: Polytropic Process, n=1.5

  19. 1 3.0 p (bar) 2b pVn=k 0.1 0.2 V (m3) Example: Polytropic Process, n=1

  20. 1 3.0 2c p (bar) pVn=k 0.1 0.2 V (m3) Example: Polytropic Process, n=0

  21. Reversibility • Process are idealized as reversible • The process can be reversed with a return to the original state. • No dissipative effects • No production of entropy • Irreversible work • Friction work and viscous work always oppose mechanical work • Transfer of heat through a finite ∆T

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