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Thermodynamics Lecture on Heat and Energy Transfer in Materials

Understand thermal energy exchange, Ideal Gas Law, specific heats of gases and solids, adiabatic processes, and 1st Law of Thermodynamics concepts. Complete HW11 and read Chapter 18 for discussion. Explore various gas processes on pV diagrams.

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Thermodynamics Lecture on Heat and Energy Transfer in Materials

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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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