1. Apply heat and energy transfer processes Recognize adiabatic processes
Lecture 23, Nov. 19
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 Sunday (11:59 PM)
For Wednesday, Read through all of Chapter 18 1

2. Exam III Room assignments
613  Room 2223 Koki
601  Room 2241 Matt 603  Room 2241 Heming 608  Room 2241 Matt 609  Room 2241 Heming 607  Room 2241 Koki
And all others in Room

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

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

5. Exercise Identify processes
Identify the nature of paths 1, 2, 3 and 4
(A) Isobaric
(B) Isothermal
(C) Isochoric
(D) Adiabatic p V 1 2 3 4 T1 T2 T3 T4

6. WA = WB but neither is zero
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 by process B.
WA > WB
WA < WB
WA = WB = 0
WA = WB but neither is zero
Answer: A
ON BY
A 1  3 W12 = 0 (isochoric)
B 1  2 W12 = -½ (p1+p2)(V2-V1) < W12 > 0
B 2  3 W23 = -½ (p2+p3)(V1-V2) > W23 < 0
B 1 = ½ (p3 - p1)(V2-V1) > < 0

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 CV ΔT

8. 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.

9. 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?
(b) Steam burns the skin worse than hot water because the latent heat of vaporization is released as well.
How much heat H1 is transferred to the skin by 25.0 g of steam?
The latent heat of vaporization for steam is L = 2256 kJ/kg.
H1 = kg x 2256 kJ/kg = 63.1 kJ
How much heat H2 is transferred to the skin by 25.0 g of water?
H2 = kg x 63 K x 4190 J/ kg K = 6.7 kJ

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

11. 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)

12. Thermal Conductivities
J/s m °C
J/s m °C
J/s m °C
Aluminum
238
Air
0.0234
Asbestos
0.25
Copper
397
Helium
0.138
Concrete
1.3
Gold
314
Hydrogen
0.172
Glass
0.84
Iron
79.5
Nitrogen
Ice
1.6
Lead
34.7
Oxygen
0.0238
Water
0.60
Silver
427
Rubber
0.2
Wood
0.10

13. 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?
100 C
300 C
(B)
(C)
(A)
Position
Temperature
Position
Temperature
Position
Temperature

14. 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)

15. 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

16. 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.)

17. Ch. 18, Macro-micro connection Molecular 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.

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

19. Molecular Speeds and Collisions

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

21. 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)

22. Lecture 23, Nov. 19 Assignment HW10, Due Sunday (11:59 PM)
For Wednesday, Read through all of Chapter 18
Following slides are for Wednesday 1

23. Kinetic energy of a gas
The average kinetic energy of the molecules of an ideal gas at 10°C has the value K1. At what temperature T1 (in degrees Celsius) will the average kinetic energy of the same gas be twice this value, 2K1?
(A) T1 = 20°C
(B) T1 = 293°C
(C) T1 = 100°C
The molecules in an ideal gas at 10°C have a root-mean-square (rms) speed vrms.
At what temperature T2 (in degrees Celsius) will the molecules have twice the rms speed, 2vrms?
(A) T2 = 859°C
(B) T2 = 20°C
(C) T2 = 786°C

24. Exercise
Consider a fixed volume of ideal gas. When N or T is doubled the pressure increases by a factor of 2.
1. If T is doubled, what happens to the rate at which a single molecule in the gas has a wall bounce?
(A) x1.4
(B) x2
(C) x4
2. If N is doubled, what happens to the rate at which a single molecule in the gas has a wall bounce?
(B) x1.4
(A) x1
(C) x2

25. Degrees of freedom or “modes”
Degrees of freedom or “modes of energy storage in the system” can be: Translational for a monoatomic gas (translation along x, y, z axes, energy stored is only kinetic) NO potential energy
Rotational for a diatomic gas (rotation about x, y, z axes, energy stored is only kinetic)
Vibrational for a diatomic gas (two atoms joined by a spring-like molecular bond vibrate back and forth, both potential and kinetic energy are stored in this vibration)
In a solid, each atom has microscopic translational kinetic energy and microscopic potential energy along all three axes.

26. Degrees of freedom or “modes”
A monoatomic gas only has 3 degrees of freedom (just K, kinetic)
A typical diatomic gas has 5 accessible degrees of freedom at room temperature, 3 translational (K) and 2 rotational (K)
At high temperatures there are two more, vibrational with K and U
A monomolecular solid has 6 degrees of freedom
3 translational (K), 3 vibrational (U)

27. The Equipartition Theorem
The equipartition theorem tells us how collisions distribute the energy in the system. Energy is stored equally in each degree of freedom of the system.
The thermal energy of each degree of freedom is:
Eth = ½ NkBT = ½ nRT
A monoatomic gas has 3 degrees of freedom
A diatomic gas has 5 degrees of freedom
A solid has 6 degrees of freedom
Molar specific heats can be predicted from the thermal energy, because

28. Exercise
A gas at temperature T is mixture of hydrogen and helium gas. Which atoms have more KE (on average)?
(A) H (B) He (C) Both have same KE
How many degrees of freedom in a 1D simple harmonic oscillator?
(A) 1 (B) 2 (C) 3 (D) 4 (E) Some other number