LNK2LRN™ 2007/08

AP Physics B

December 14 to 21.

Chapter 14 & 15: The Ideal Gas Law,

Kinetic Theory, and Thermodynamics.

Plans for the Week and Assignments:

1. FRIDAY(12/14): Molecular Mass, Ideal Gas Law, Kinetic Theory of

Gases, and Diffusion. HW: Read pages 394-409 and solve prob. 1, 3, 9,

11, 28, 29, and 39 on pages 411-413.

2. MONDAY(12/17): Thermodynamic Systems, the Zeroth Law, the

First Law, Thermal Processes, and Specific Heat Capacities. HW: Read

pages 417-428 and solve prob. 2, 7, 18, 30, and 40 on pages 444-446.

3. TUESDAY(12/18): The Second Law, Heat Engines, Carnot's

Principle, Entropy, and Review . HW: Read pages 428-439 and solve

prob. 46, 47, 57, 58, and 68 on pages 446-447.

4. WEDNESDAY(12/19): TEST on Chap.14&15 - Ideal gas Law, Kinetic

Theory, and Thermodynamics. HW: Go to web-site for notes

Chapters 16 & 17 - Waves and Sound.

5. THURSDAY(12/20): LAB on Boyles Law. HW: Process lab data and

write lab report.

6. FRIDAY(12/21): Post-Lab Discussion. Lab Report is due by end of

class. HW: Have a safe and restful Holiday Break!

 

Very Important: If you have any questions or miss a class, see

me before school (8:00 - 8:30 AM), during Lunch, 7th hour, or

after school. Best to send an email to rpersin@fau.edu.

 

WEBSITE NOTES: Ch. 14 & 15 - The Ideal Gas Law, Kinetic Theory,

and Thermodynamics.

1. Each element in the periodic table is assigned an atomic mass. One atomic

mass unit (u) is exactly one-twelfth the mass of an atom of carbon-12.

The mass of a molecule is the sum of the atomic masses of its atoms.

2. The number of moles n contained in a sample is equal to the number of

particles N (atoms or molecules) in the sample divided by the number of

particles per mole NA. We then have the equation n = N/NA, where

NA = 6.022x1023 particles per mole, known as Avogadro’s Number, from

Amedeo Avogadro (1776-1856), Turin, Italy.

3. The number of moles is also equal to the mass m of the sample (expressed

in grams) divided by the mass per mole (expressed in grams per mole ). This

gives us the equation n = m/(mass per mole). The mass per mole (in g/mol)

of a substance has the same numerical value as the atomic or molecular mass

of one of its particles (in atomic mass units).

4. The mass of a particle (in grams) can be obtained by dividing the mass per

mole (in g/mol) by Avogadro's number: mparticle = mass per mole/NA.

5. The ideal gas law relates the absolute pressure P, the volume V, the number

n of moles, and the Kelvin temperature T of an ideal gas, or PV = nRT, here

we have R = 8.31 J/(mol∙K), the universal gas constant. An ideal gas is one

that within a range of densities, temperature, volume, and pressure have a

simple relationship.

6. An alternative form of the ideal gas law is PV = NkT, where N is the number

of particles and k = R/NA = 1.38x10-23 J/K , a constant named after Ludwig

Boltzmann (1844-1906), Austria, who developed the branch of Physics known

as Statistical Mechanics.

7. Recall from Chemistry that a real gas behaves like an ideal gas if its density

is low enough that its particles do not interact, except via elastic collisions.

All gas laws use the absolute temperature unit, the Kelvin (K), named after

William Thomson, Lord Kelvin (1824-1907). Water freezes at 273.15 K and

boils at 373.15 K, with 0.00 K being absolute zero.

8. When a gas is kept at constant temperature, its pressure is inversely

proportional to the volume. This is Boyle's Law PiVi = PfVf , named after Robert

Boyle (1627-1691) from Ireland.

9. Also, when the pressure is kept constant, the volume is directly proportional

to the temperature. This is the law of Charles and Guy-Lussac Vi/Ti = Vf/Tf ,

from Jacques Charles (1746-1823) and Joseph Louis Guy-Lussac (1778-1850),

both from France.

10. Temperature is a quantity proportional to the average kinetic energy of the

particles. This is based on Kinetic Theory, which assumes that (i) all matter is

composed of tiny particles (atoms or molecules), and (ii) these particles are in

constant motion.

11. The equation that we applies here is KEavg = ½ mv2rms = 3/2 kT, where

vrms is the root-mean-square speed of the particles, derived statistically.

The internal energy U of n moles of a monatomic ideal gas is U = 3/2 nRT.

12. Diffusion is the process by which solute molecules move through a solvent

from an area of higher concentration to an area of lower concentration. Fick’s

Law, named after Adolf Eugen Fick (1829-1901), Germany, states that the mass

of a solute that diffuses in time through a channel of known length and

cross-sectional area is given by m = (D·A·ΔC)t/L . In this equation, ΔC is the

solute concentration difference between the ends of the channel, and D is the

diffusion constant.

13. Thermodynamics is the study of heat and how it relates to the other forms

of energy (mechanical, light, sound, electric, magnetic, atomic, and nuclear).

The Zeroth Law of Thermodynamics states that two systems are in thermal

equilibrium if there is no net heat flow between them when they are brought

into thermal contact.

14. The First Law of Thermodynamics states that the total increase in thermal

energy of a system is equal to the sum of the heat added to it and the work

done on it, which is given by the equation ΔU = (Uf -Ui) = Q-W.

15. A thermal process is considered quasi-static when it occurs slowly enough

that a uniform pressure and temperature exist throughout the system at all

times. The work done in any kind of quasi-static process is given by the area

under the pressure versus volume graph.

16. An isobaric process is one that occurs at constant pressure. The work done

when a system changes at constant pressure from initial to final volume is

given by the equation W = P·ΔV = P(Vf -Vi).

17. An isochoric process is done at constant volume and no work is done. An

isothermal process is done at constant temperature. An adiabatic process

takes place without the transfer of heat.

18. When n moles of an ideal gas change quasi-statically from an initial to a

final volume at a constant Kelvin temperature, the work done is given by

W = nRT·ln(Vf /Vi).

19. When n moles of an ideal gas change quasi-statically and adiabatically

from an initial to a final Kelvin temperature, the work done is according to

W = 3/2 nR(Ti -Tf).

20. During an adiabatic process, and in addition to the Ideal Gas Law, an

ideal gas obeys the relation PiViγ = PfVfγ, where γ = cp/cv, which is the ratio

of specific heat capacities at constant pressure and constant volume.

21. The molar specific heat capacity of a substance determines how much

heat is added or removed when the temperature of n moles of the substance

changes. This is given by the equation Q = C·n·ΔT.

22. For a monatomic ideal gas, the molar specific heat capacities at

constant pressure and constant volume are, respectively, CP = 5/2 R and

CV = 3/2 R, where R is the Ideal Gas Constant equal to 8.31 J/(mol·K).

23. For any type of an ideal gas, the difference between CP and CV is R,

or CP - CV = R.

24. There are many equivalent statements for the Second Law of

Thermodynamics. In terms of heat flow, the second law declares that heat

flows spontaneously from a substance at higher temperature to a substance

at lower temperature.

25. The second law also states that natural processes always go in a

direction that increases the entropy, S, unavailable energy, or disorder, of a

system. ΔS = Q – W.

26. A heat engine continuously converts thermal energy to mechanical energy

and does work. The efficiency, e, of a heat engine is expressed by the

equation e = (Work done)/(Input heat) = W/QH.

27. Conservation of energy requires that the input heat of magnitude QH

must be equal to the work done plus the heat of magnitude QC rejected or

expelled to a cold reservoir. This gives us QH = W + QC. By combining the

previous two equations we arrive at the result, e = 1 – (QC / QH ).

28. A reversible process is one in which the both system and its environment

can be returned to exactly the same states they were in before the process

occurred. An alternate statement for the second law was stated by French

engineer, Sadi Carnot (1796-1832).

29. Carnot’s principle states that no irreversible engine operating between

two reservoirs at constant temperature can have a greater efficiency than a

reversible engine operating between the same temperatures. Furthermore,

all reversible engines operating between the same temperatures have the

same efficiency.

30. A Carnot engine is a reversible engine in which all input heat QH

originates from a hot reservoir at a single Kelvin temperature, and all rejected

heat QC goes into a cold reservoir also at a single Kelvin temperature. For the

Carnot engine, we have QC/QH = TC/TH.

31. This gives an equation for the maximum efficiency that an engine can have

operating between two fixed temperatures. e Carnot = 1 - TC/TH.

32. A heat pump, air conditioner, or refrigerator uses mechanical energy to

transfer heat from an area of lower to higher temperature. These are governed

by the Law of Conservation of Energy with QH = W + QC.

33. The coefficient of performance of a refrigerator or air conditioner is given

by the equation Coefficient of performance = QC /W. For the heat pump

we have a similar relationship, Coefficient of performance = QH/W.

34. The change in entropy, ΔS, for a process in which heat enters or leaves a

system reversibly at a constant Kelvin temperature is ΔS = (Q/T)R, where the

subscript R stands for "reversible."

35. In terms of entropy, the second law states that the total entropy of the

universe does not change when a reversible process occurs (ΔSuniverse = 0 J/K),

and increases when an irreversible process occurs (ΔS > 0 J/K).

36. Irreversible processes cause energy to be made unavailable for the

performance of work. This energy is given by Wunavailable = To·ΔSuniverse where

ΔSuniverse is the total entropy change in the universe and To is the Kelvin

temperature of the coldest reservoir into which heat can be rejected.

37. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.

38. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.

View the PowerPoint.

 

animated open door gifARCHIVES:   CH.1   CH.2  CH.3  CH.4&5  CH.6&7

CH.8&9  CH.10  CH.11  CH.12&13

USEFUL LINKS AND WEBSITES TO VISIT:    

LINK TO YOUR TEXTBOOK 

LAB ABSTRACT

ENGINEERS EDGE

 EDLINE

THERMODYNAMICS

 

IDEAL GAS LAW

 

HEAT ENGINES

ENTROPY

 And Always Remember... 

"From  Newtonian Mechanics,

 Through Quantum Theory,  

Without Knowledge of Physics,  

Life Would Be Dreary."

Homework Help? 

Click below to check your solutions.

Chapter 14(1)     Chapter 14(2)

Chapter 15(1)     Chapter 15(2)

Chapter 15(3)