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Short Version : 18. Heat, Work, & First Law of Thermodynamics

Short Version : 18. Heat, Work, & First Law of Thermodynamics. 18.1. The 1 st Law of Thermodynamics. PE of falling weight  KE of paddle  Heat in water. Either heating or stirring can raise T of the water. 1 st Law of Thermodynamics :

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Short Version : 18. Heat, Work, & First Law of Thermodynamics

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  1. Short Version : 18. Heat, Work, & First Law of Thermodynamics

  2. 18.1. The 1st Law of Thermodynamics PE of falling weight  KE of paddle  Heat in water Either heating or stirring can raise T of the water. 1st Law of Thermodynamics: Increase in internal energy = Heatadded  Work done e.g., U, T, P, V, … Not Q, W, … Thermodynamic state variable = variable independent of history. Joule’s apparatus

  3. 18.2. Thermodynamic Processes Quasi-static process: Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium. Reversible process: Any changes induced by the process in the universe (system + environment) can be removed by retracing its path. Reversible processes must be quasi-static. Twater = Tgas & rises slowly Irreversible process: Part or whole of process is not reversible. e.g., any processes involving friction, free expansion of gas …. system always in thermodynamic equilibrium

  4. Work & Volume Changes 面積 Work done by gas on piston

  5. Isothermal Processes Isothermal process: T = constant.  Isothermal processes on ideal gas

  6. Constant-Volume Processes & Specific Heat Constant-volume process ( isometric, isochoric, isovolumic ) : V = constant  CV = molar specific heat at constant volume  isometric processes Ideal gas: U = U(T)  for all processes Non-ideal gas: only for isometric processes

  7. Isobaric Processes & Specific Heat Isobaric Process : constant P Isotherms CP = molar specific heat at constant pressure isobaric processes Ideal gas, isobaric :  Ideal gas

  8. Adiabatic Processes Adiabatic process: Q = constant e.g., insulated system, quick changes like combustion, … adiabat, ideal gas Tactics 18.1.  Prob. 66 Adiabatic: larger p Prob. 62 cdf

  9. TACTIC 18.1. Adiabatic Equation Ideal gas, any process: Adiabatic process:   

  10. Example 18.3. Diesel Power Fuel ignites in a diesel engine from the heat of compression (no spark plug needed). Compression is fast enough to be adiabatic. If the ignit temperature is 500C, what compression ratio Vmax / Vmin is needed? Air’s specific heat ratio is  = 1.4, & before the compression the air is at 20 C.

  11. Ideal Gas Processes

  12. Cyclic Processes Cyclic Process : system returns to same thermodynamic state periodically.

  13. Example 18.4. Finding the Work An ideal gas with  = 1.4 occupies 4.0 L at 300 K & 100 kPa pressure. It’s compressed adiabatically to ¼ of original volume, then cooled at constant V back to 300 K, & finally allowed to expand isothermally to its original V. How much work is done on the gas? AB (adiabatic): BC (isometric): CA (isothermal): work done by gas:

  14. 18.3. Specific Heats of an Ideal Gas Ideal gas:   Experimental values( room T ): For monatomic gases,   5/3, e.g., He, Ne, Ar, …. For diatomic gases,   7/5 = 1.4, CV = 5R/2, e.g., H2 , O2 , N2 , …. For tri-atomic gases,   1.3, CV = 3.4R, e.g., SO2 , NO2 , …. Degrees of freedom (DoF) = number of independent coordinates required to describe the system Single atom: DoF = 3 (transl) For low T ( vib modes not active ) : Rigid diatomic molecule : DoF = 5 (3 transl + 2 rot) Rigid triatomic molecule : DoF = 6 (3 transl + 3 rot)

  15. The Equipartition Theorem Equipartition theorem( kinetic energy version): For a system in thermodynamic equilibrium, each degree of freedom of a rigid molecule contributes ½ kT to its average energy. Equipartition theorem( general version): For a system in thermodynamic equilibrium, each degree of freedom described by a quadratic term in the energy contributes ½ kT to its average energy.

  16. Example 18.5. Gas Mixture A gas mixture consists of 2.0 mol of oxygen (O2) & 1.0 mol of Argon (Ar). Find the volume specific heat of the mixture.

  17. Quantum Effects Quantum effect: Each mechanism has a threshold energy. Etransl < Erot < Evib rotation+Translation+vibration rotation+Translation Translation CV of H2 gas as function of T. Below 20 K hydrogen is liquid, above 3200 K it dissociates into individual atoms.

  18. Reprise Quasi-static process : Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium. Reversible process: Any changes induced by the process in the universe (system + environment) can be removed by retracing its path. Dissipative work: Work done on system without changing its configuration, irreversible. Insulated gas a c : Free expansion with no dissipative work. c b : Adiabatic. a d : Adiabatic. d b : Free expansion with no dissipative work. a e : Adiabatic. e b : Adiabatic dissipative work. 1st law: The net adiabatic work done in all 3 processes are equal (shaded areas are equal).

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