Swain Hall West- 1st Floor

DVB’s office

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Web site: http://physics.indiana.edu/~courses/p340/S10/

Swain Hall West- 2nd Floor

AI office on third floor 340

LibraryPhysics Forum Lectures

CALM system

NOTE: To get full credit for the semester’s CALM portion of the course, you need to answer 75% of the semester’s CALM questions.

P340 Lecture 2-- CALM• Concisely describe the fundamental physical

significance/meaning of the absolute temperature of an object. (no response from 3 students; 2 others gave answers not covered by the following)• Average kinetic energy of vibrations in a quantity of matter where

absolute zero corresponds to no vibration . (4 responses like this).

• Temperature is hotness measured on some definite scale (where the concept of hotness is shown when two objects are in thermal contact;(3 responses)

• The last of these is the best, (right from the book), but what is “Hotness”. Temperature is that quantity that tells us how heat flows when two objects are put into thermal contact

P340 Lecture 2- Temperature• THERMAL EQUILIBRIUM:

• Two systems are said to be in thermal equilibrium if, when they are brought into thermal contact, NO NET HEAT EXCHANGE takes place.

• Zeroth law of thermodynamics• If two systems (A and C) are both in thermal equilibrium with a third

system (B), then they are in thermal equilibrium with each other. (conventional statement)

• “There exist things called thermometers” (DVB’s statement; thermometers allow you to predict how and whether heat will flow when two objects are brought into thermal contact, but quantifying their “hotness”)

• Kelvin Temperature scale is defined as follows:• 0 K is absolute zero; an object that CANNOT act as a source of heat

for any other object is at absolute zero (more on this later).

• 273.16 K is the triple point of pure water.

P340 Lecture 2• THERMOMETERS:

• Primary (PT): Some easily measureable physical quantity is a well-understood function of temperature

– Ideal gas (constant volume) thermometer: P =(N/V)kBT

– Black Body Radiation: (I(n) =(8ph/c3)(1/(exp(hn/kBT) -1))

– Paramagnetic Salt magnetization: (M = cH/(T –q))

– Johnson Noise of a resistor: (vrms = (4kBTR)1/2

• Secondary (ST): Some easily measureable physical quantity is a well-characterized function of temperature

– Thermal expansion (Hg, alcohol, bimetallic strips, etc.)

– Electrical resistance (of Pt, Ge, carbon, Si diodes etc.)

– Thermocouples

• The difference is the universality of the relationship between the measured quantity and the temperature. PT’s tend to be complicated to use, most often one uses calibrated ST’s.

One or more commonly a few points needed for calibration;NIST worries about these

P340 Lecture 2“Practical Thermometry”

• International Temperature Scale (ITS-90)

• This is the accepted standard against which secondary thermometers are typically calibrated (it deviates from absolute temperature in certain regions by several mK).• 0.65-5K (3He or 4He equil. vapor pressure over liquid)

• 3.0 to 24.5561 K (He gas thermometer calibrated at defined fixed points)

• 13.8033 to 1234.93 K (Pt resistance thermometer calibrated at defined fixed points with set interpolation scheme).

• Above 1234.93 K: Planck radiation law.

P340 Lecture 2“CMB fit to BB spectrum”

http://www.astro.ucla.edu/~wright/CMB.html

• The plot on the right shows data from the FIRAS instrument on the original COBE satellite experiment. The measurement of interest here was the set of residuals (i.e. the lower plot of the differences between the measured spectrum and that of a true black body)

• The curves correspond to various non-ideal BB spectra:• 100 ppm reflector (e)• Effect of hot electrons adding extra

60ppm of energy just about 1000 yrs after the big bang (m just before 1000 yrs, y just after)

P340 Lecture 3(Review)

• The macroscopic state of the system is defined by a number of parameters, some are external parameters (determine the microscopic states available to the system, e.g. total energy, volume, number of particles, external magnetic or electric fields etc.), and some are averages over microscopic properties of the system (pressure, magnetization, electric polarization, …)

• 1st law: Internal energy can change only through heat being exchanged or work being done.

• Oth law: Temperature tells you what direction heat will flow (and if it will flow).• Heat capacity: describes how much heat exchange is needed to effect a given

change in temperature.• “Specific Heat” is the heat capacity per unit mass (or volume, or molecule

etc.)• Many quantities in thermodynamics (e.g. work done, heat transferred, specific

heat, compressibility, …) depend on the particular process involved (what path you take through parameter space; what things you keep fixed etc.).• E.g. CP is NOT the same as CV

• For an ideal gas CV= 1.5 NkB and CP = 2.5 NkB In general: CP = CV + NkB

P340 Lecture 3(Example:)

NOTE: An adiabatic path, is one in which NO heat is exchanged with the outside world; an isothermal path is one along which the Temperature is held fixed.(In all cases, we only consider “quasi-static” changes , ones that are slow enough to consider the system to always be in a well-defined macrostate (equilibrium at all times).

P340 Lecture 3(Example:)

NOTE: An adiabatic path, is one in which NO heat is exchanged with the outside world; an isothermal path is one along which the Temperature is held fixed.(In all cases, we only consider “quasi-static” changes , ones that are slow enough to consider the system to always be in a well-defined macrostate (equilibrium at all times).

How does the temperature here compare to To?

=To

(Po,Vo)

P340 Lecture 3“Probability and Statistics”

• Bernoulli Trials• REPEATED, IDENTICAL, INDEPENDENT, RANDOM

trials for which there are two outcomes (“success” prob.=p; “failure” prob=q) – EXAMPLES: Coin tosses, queuing problems, radioactive

decay, scattering experiments, 1-D random walk,…

• A question of fundamental importance in these problems is: Suppose I have N such trials, what is the probability that I have “n” successes? The answer is:

P(n) = N!/[n!(N-n)!] pn(1-p)N-n

We will spend a bit of time looking at this distribution.