18. Heat, Work, & First Law of Thermodynamics

1. 18. Heat, Work, & First Law of Thermodynamics The 1st Law of Thermodynamics Thermodynamic Processes Specific Heats of an Ideal Gas

2. A jet aircraft engine converts the energy of burning fuel into mechanical energy. How does energy conservation apply in this process? E combustion = E mech + Q waste

3. 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

4. Example 18.1. Thermal Pollution The reactor in a nuclear power plant supplied energy at the rate of 3.0 GW, boiling water to produce steam that turns a turbine-generator. The spent steam is then condensed through thermal contact with water taken from a river. If the power plant produces electrical energy at the rate of 1.0 GW, at what rate is heat transferred to the river? 1st law  From standpoint of power plant: ( loses heat to river )

5. 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

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

7. GOT IT? 18.1. • Two identical gas-cylinder systems are taken from the same initial state to the same final state, but by different processes. • Which are the same in both cases: • the work done on or by the gas, • the heat added or removed, or • the change in internal energy?

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

9. Example 18.2. Bubbles! A scuba diver is 25 m down, where the pressure is 3.5 atm ( 350 kPa ). The air she exhales forms bubbles 8.0 mm in radius. How much work does each bubble do as it arises to the surface, assuming the bubbles remain at 300 K. T = const 

10. 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

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

12. 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

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

14. Conceptual Example 18.1. Ideal-Gas Law vs Adiabatic Equation The ideal gas law says p V = n R T, but the adiabatic equation says p V  = const. Which is right ? Both are right. The adiabatic equation is a special case where T V +1

15. Making the Connection • Suppose you halve the volume of an ideal gas with  = 1.4. • What happens to the pressure if the process is • isothermal and • adiabatic? • Ans: • pV = const  p= 2 p0(doubles) • p V = const  p = p02  = 2.64 p0

16. 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.

17. Application: Smog Alert! Air is poor heat conductor  convection is adiabatic. If rising air cools slower than surrounding air, pollution rises high & can be dispersed. Otherwise, smog.

18. GOT IT? 18.2. • Name the basic thermodynamic process involved when each of the following is done to a piston-cylinder system containing ideal gas, • & tell also whether T, p, V, & U increase or decrease. • the piston is lock in place& a flame is applied to the bottom of the cylinder, • the cylinder is completely insulated & the piston is pushed downward, • the piston is exposed to atmospheric pressure & is free to move, while the cylinder is cooled by placing it on a block of ice. • isometric; T , p, V =const, U . • adiabatic; T , p, V , U . • isobaric; T , p=const, V , U .

19. Ideal Gas Processes

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

21. 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:

22. 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)

23. 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.

24. 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.

25. 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.

26. 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).