Lecture 24

1. Lecture 24 Goals: • Chapter 17 • Apply heat and energy transfer processes • Recognize adiabatic processes • 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 • HW10, Due Wednesday 9:00 AM • For Thursday, Read through all of Chapter 18

2. p V T1 3 T2 T3 T4 Isothermal processes • Work done when PV = nRT = constant  P = nRT / V

3. p 4 V 2 T1 3 1 T2 T3 T4 Adiabatic Processes • 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.

4. Work and Ideal Gas Processes (on system) • Isothermal • Isobaric • Isochoric • FYI: Adiabatic (and reversible)

5. Combinations of Isothermal & Adiabatic Processes All engines employ a thermodynamic cycle W = ± (area under each pV curve) Wcycle = area shaded in turquoise Watch sign of the work!

6. Relationship between energy transfer and T

7. 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

8. 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)

9. 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

10. 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

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

12. 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

13. Exercise Latent Heat • Most people were at least once burned by hot water or steam. • Assume that water and steam, initially at 100°C, are cooled down to skin temperature, 37°C, when they come in contact with your skin. Assume that the steam condenses extremely fast, and that the specific heat c = 4190 J/ kg K is constant for both liquid water and steam. • Under these conditions, which of the following statements is true? (a) Steam burns the skin worse than hot water because the thermal conductivity of steam is much higher than that of liquid water. (b) Steam burns the skin worse than hot water because the latent heat of vaporization is released as well. (c) Hot water burns the skin worse than steam because the thermal conductivity of hot water is much higher than that of steam. (d) Hot water and steam both burn skin about equally badly.

14. For a material of cross-section area A and length L, spanning a temperature difference ΔT = TH – TC, the rate of heat transfer is Q / t = k A DT / x where k is the thermal conductivity, which characterizes whether the material is a good conductor of heat or a poor conductor. Energy transfer mechanisms • Thermal conduction (or conduction) • Convection • Thermal Radiation

15. 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)

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

17. Temperature Temperature Temperature Position Position Position Exercise Thermal Conduction • Two thermal conductors (possibly inhomogeneous) 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) (A)

18. 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)

19. 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

20. Anti-global warming or the nuclear winter scenario • Assume P/A = I = 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 = I p r2  T = [I / (4 x  )]¼ • s =5.710-8 W/m2 K4 • T = 277 K (A little on the chilly side.)

21. Ch. 18, Macro-micro connectionMolecular Speeds and Collisions • A real gas consists of a vast number of molecules, each moving randomly and undergoing millions of collisions every second. • Despite the apparent chaos, averages, such as the average number of molecules in the speed range 600 to 700 m/s, have precise, predictable values. • The “micro/macro” connection is built on the idea that the macroscopic properties of a system, such as temperature or pressure, are related to the average behavior of the atoms and molecules.

22. Molecular Speeds and Collisions A view of a Fermi chopper

23. Molecular Speeds and Collisions

24. Mean Free Path If a molecule has Ncollcollisions as it travels distance L, the average distance between collisions, which is called the mean free pathλ(lowercase Greek lambda), is

25. Macro-micro connection • Assumptions for ideal gas: • # of molecules N is large • They obey Newton’s laws • Short-range interactions with elastic collisions • Elastic collisions with walls (an impulse…..pressure) • What we call temperature T is a direct measure of the average translational kinetic energy • What we call pressure p is a direct measure of the number density of molecules, and how fast they are moving (vrms)

26. Lecture 24 • Assignment • HW10, Due Wednesday (9:00 AM) • Tuesday review • Reading assignment through all of Chapter 18