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Lecture 24

Lecture 24. Goals:. Chapter 17 Employ heat (Q) and energy transfer in materials Recognize adiabatic processes (i.e., Q=0) Chapter 18 Follow the connection between temperature, thermal energy, and the average translational kinetic energy molecules

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Lecture 24

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  1. Lecture 24 Goals: • Chapter 17 • Employ heat (Q) and energy transfer in materials • Recognize adiabatic processes (i.e., Q=0) • Chapter 18 • Follow the connection between temperature, thermal energy, and the average translational kinetic energy molecules • Understand the molecular basis for pressure and the ideal-gas law. • To predict the molar specific heats of gases and solids. • Assignment • HW11, Due Wednesday 9:00 AM • For Thursday, Read through all of Chapter 18

  2. 1st Law of Thermodynamics • Work W and heat Q depend on process by which the system is changed (path dependent). • The change of energy in the system, ΔEth depends only on the total energy exchanged W+Q, noton the process. ΔEth=W + Q (if DK &DU =0 ) W & Q with respect to the system

  3. 1st Law: Work & Heat • Work doneon system (an ideal gas….notice minus sign, V is in reference to the system) • Won system < 0 Moving left to right [where (Vf > Vi)] • If ideal gas, pV = nRT • Wby system > 0 Moving left to right

  4. 1st Law: Work & Heat • Work: • Depends on the path taken in the pV-diagram (It is not just the destination but the path…) • Won system > 0 Moving right to left

  5. W = - p DV ???? W = 0 ???? p V Paths on the pV diagram (with an idea gas) (1) Isobaric (2) Isothermal (3) Isochoric (4) Adiabatic 1 Ideal gas 3 T1 2 T2 4 T3 T4

  6. p V T1 3 T2 T3 T4 Isothermal processes (in an ideal gas) • Work done when PV = nRT = constant  P = nRT / V For this we need access to thermal energy

  7. p 4 V 2 T1 3 1 T2 T3 T4 Adiabatic Processes (in an ideal gas) • An adiabatic process is process in which there is no thermal energy transfer to or from a system (Q = 0) • A reversibleadiabatic process involves a “worked” expansion in which we can return all of the energy transferred. • In this case PVg = const. • All real processes are not. • We need to know Cp & CV

  8. Work and Ideal Gas Processes (on system) • Isothermal • Isobaric • Isochoric • FYI: Adiabatic (and reversible) PVg = const.

  9. Two process are shown that take an ideal gas from state 1 to state 3. (“by” means “by the system on the world”) Compare the work done by process A to the work done byprocess B. p3 • WA > WB • WA < WB • WA = WB = 0 • WA = WB but neither is zero p2 p1 ON BY A 1  3 W12 = 0 (isochoric) B 1  2 W12 = -½ (p1+p2)(V2-V1) < 0 -W12 > 0 B 2  3 W23 = -½ (p2+p3)(V1-V2) > 0 -W23 < 0 B 1 3 = ½ (p3 - p1)(V2-V1) > 0 < 0

  10. Two process are shown that take an ideal gas from state 1 to state 3. Compare the work done by process A to the work done byprocess B. • WA > WB • WA < WB • WA = WB = 0 • WA = WB but neither is zero ON BY A 1  3 W12 = 0 (isochoric) B 1  2 W12 = -½ (p1+p2)(V2-V1) < 0 -W12 > 0 B 2  3 W23 = -½ (p2+p3)(V1-V2) > 0 -W23 < 0 B 1 3 = ½ (p3 - p1)(V2-V1) > 0 < 0

  11. Both Q and W can change T • We know how work changes the mechanical energy of a solid “system” • Here our system is an ideal gas….only the temperature can change • For real materials we can change the temperature or the state • We must quantify the response of a system to thermal energy transfer (Q)

  12. What about Q? What are the relationships between DETh and T. Specific Heat Latent Heat Latent Heat

  13. Heat and Latent Heat • Latent heat of transformation L is the energy required for 1 kg of substance to undergo a phase change. (J / kg) Q = ±ML • Specific heat c of a substance is the energy required to raise the temperature of 1 kg by 1 K. (Units: J / K kg ) Q = M c ΔT • Molar specific heat C of a gas at constant volume is the energy required to raise the temperature of 1 mol by 1 K. Q = n CVΔT If a phase transition involved then the heat transferred is Q = ±ML+M c ΔT

  14. Q : Latent heat and specific heat • The molar specific heat of gasses depends on the process path • CV= molar specific heat at constant volume • Cp= molar specific heat at constant pressure • Cp= CV+R (R is the universal gas constant)

  15. Latent Heat • Most people were at least once burned by hot water or steam. • An equal amount (by mass) of boiling water and steam contact your skin. • Which is more dangerous, the water or the steam?

  16. Mechanical equivalent of heat • Heating liquid water: • Q = amount of heat that must be supplied to raise the temperature by an amount  T . • [Q] = Joules or calories. • calorie: energy to raise 1 g of water from 14.5 to 15.5 °C (James Prescott Joule found the mechanical equivalent of heat.) 1 cal = 4.186 J 1 kcal = 1 cal = 4186 J Sign convention: +Q : heat gained - Q : heat lost

  17. Exercise • The specific heat (Q = M c ΔT) of aluminum is about twice that of iron. Consider two blocks of equal mass, one made of aluminum and the other one made of iron, initially in thermal equilibrium. • Heat is added to each block at the same constant rate until it reaches a temperature of 500 K. Which of the following statements is true? (a) The iron takes less time than the aluminum to reach 500 K (b) The aluminum takes less time than the iron to reach 500 K (c) The two blocks take the same amount of time to reach 500 K

  18. Exercise • The specific heat (Q = M c ΔT) of aluminum is about twice that of iron. Consider two blocks of equal mass, one made of aluminum and the other one made of iron, initially in thermal equilibrium. • Heat is added to each block at the same constant rate until it reaches a temperature of 500 K. Which of the following statements is true? (a) The iron takes less time than the aluminum to reach 500 K (b) The aluminum takes less time than the iron to reach 500 K (c) The two blocks take the same amount of time to reach 500 K

  19. Heat and Ideal Gas Processes (on system) • Isothermal Expansion/Contraction • Isobaric • Isochoric • Adiabatic

  20. Energy transfer mechanisms • Thermal conduction (or conduction) • Convection • Thermal Radiation

  21. Energy transfer mechanisms • Thermal conduction (or conduction): • Energy transferred by direct contact. • e.g.: energy enters the water through the bottom of the pan by thermal conduction. • Important: home insulation, etc. • Rate of energy transfer ( J / s or W ) • Through a slab of area A and thickness Dx, with opposite faces at different temperatures, Tc and Th Q / t = k A (Th - Tc ) / x • k :Thermal conductivity (J / s m °C)

  22. Thermal Conductivities J/s m °C J/s m °C J/s m °C

  23. (A) Temperature Temperature Position Position Exercise Thermal Conduction • Two thermal conductors are butted together and in contact with two thermal reservoirs held at the temperatures shown. • Which of the temperature vs. position plots below is most physical? 300 C 100 C (C) (B) Temperature Position

  24. (A) Temperature Temperature Position Position Exercise Thermal Conduction • Two thermal conductors are butted together and in contact with two thermal reservoirs held at the temperatures shown. • Which of the temperature vs. position plots below is most physical? 300 C 100 C (C) (B) Temperature Position

  25. Energy transfer mechanisms • Convection: • Energy is transferred by flow of substance 1. Heating a room (air convection) 2. Warming of North Altantic by warm waters from the equatorial regions • Natural convection: from differences in density • Forced convection: from pump of fan • Radiation: • Energy is transferred by photons e.g.: infrared lamps • Stefan’s Law • s =5.710-8 W/m2 K4 , T is in Kelvin, and A is the surface area • e is a constant called the emissivity P =  A e T4 (power radiated)

  26. Minimizing Energy Transfer • The Thermos bottle, also called a Dewar flask is designed to minimize energy transfer by conduction, convection, and radiation. The standard flask is a double-walled Pyrex glass with silvered walls and the space between the walls is evacuated. Vacuum Silvered surfaces Hot or cold liquid

  27. Anti-global warming or the nuclear winter scenario • Assume P/A = P = 1340 W/m2 from the sun is incident on a thick dust cloud above the Earth and this energy is absorbed, equilibrated and then reradiated towards space where the Earth’s surface is in thermal equilibrium with cloud. Let e (the emissivity) be unity for all wavelengths of light. • What is the Earth’s temperature? • P =  A T4=  (4p r2)T4 = Pp r2  T = [P / (4 x  )]¼ • s =5.710-8 W/m2 K4 • T = 277 K (A little on the chilly side.)

  28. Lecture 24 • Assignment • HW11, Due Wednesday (9:00 AM) • Tuesday review • Reading assignment through all of Chapter 18

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