{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Lect17 - Misce ous Note llane s The end is near dont get...

This preview shows pages 1–8. Sign up to view the full content.

Lecture 17, p 1 Miscellaneous Notes The end is near – don’t get behind. All Excuses must be taken to 233 Loomis before noon, Tuesday, Nov. 30. The PHYS 213 final exam times are * 7-9 PM, Monday, Dec. 13 and * 8-10 AM, Tuesday, Dec. 14 . The deadline for changing your final exam time is 10pm, Tuesday, Nov. 30. Homework 6 is due Saturday , Dec. 4 at 8 am. Course Survey = 2 bonus points (accessible at the top of HW6)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 17, p 2 Law of Atmospheres, revisited Semiconductors Reference for this Lecture: Elements Ch 12 Reference for Lecture 19: Elements Ch 13 Lecture 17 Applications of Free Energy Minimum
Lecture 17, p 3 Thumbnail review of free energy: Equilibrium corresponds to maximum S tot = S reservoir + S small system . When we calculate S, we only need to know the temperature of the reservoir. In minimizing F (equivalent to maximizing S tot ) we don’t have to deal explicitly with S reservoir . Consider exchange of material (particles) between two containers. These are two small systems in equilibrium with a reservoir (not shown) at temperature T. In equilibrium, dF/dN 1 = 0: The derivative of free energy with respect to particle number is so important that we define a special name and symbol for it: For two subsystems exchanging Last Time Maximum Total Entropy Minimum Free Energy Equal chemical potentials 1 2 1 2 1 1 1 1 2 1 2 1 2 0 dF dF dF dF dF dN dN dN dN dN dF dF dN dN = + = - = = 1 N F = F 1 +F 2 N 1 N 2 The chemical potential of subsystem “i” i i i dF dN μ 1 2 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 17, p 4 Chemical Potential with Potential Energy The potential energy per particle, PE, makes an additional contribution N·PE to the free energy: F = U - TS. So, the chemical potential ( μ = dF/dN) gains an additional contribution: d(N·PE)/dN = PE. It’s the energy that one particle adds to the system. Examples: A ln T n kT PE n μ= + n = N/V particle density ln T n kT mgh n + ln T n kT n - ∆
Lecture 17, p 5 Question: How do the gas density n and pressure p of the gas vary with height? Compare region 2 at height h with region 1 at height 0. (equal volumes) For every state in region 1 there’s a corresponding state in region 2 with mgh more energy. Assume that the temperature is in equilibrium (T 1 =T 2 ). Write the ideal gas law like this: p = nkT. (n N / V) The Law of Atmospheres 0 h p 2 , n 2 p 1 , n 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 17, p 6 The two regions can exchange particles (molecules), so imagine that they are connected by a narrow tube. The rest of the atmosphere is the thermal reservoir. Equilibrium: μ 1 = 2 Chemical potential (ideal gas): Solution: Ideal gas law: p/n = kT (T 1 = T 2 in equilibrium) 1 2 2 1 2 1 / ln ln mgh ln T T mgh kT n n kT kT n n n kT mgh n n n e - = + = - = 1 1 2 2 ln ln mgh T T n kT n n kT n = = + The Law of Atmospheres (2) p 2 N 2 h p 1 N 1 2 1 / mgh kT p p e - =
Lecture 17, p 7 Electrons in Semiconductors In many materials, electrons cannot have every conceivable energy. There valence band ”) and a high energy range (the A “gap” of disallowed energies separates them. (The reason for the gap is a Physics 214 topic.) At T = 0, every valence band state is occupied. (S=0. Why? ) At T 0,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 26

Lect17 - Misce ous Note llane s The end is near dont get...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online