UB, Phy101: Chapter 14, Pg 1

Okay, so I was watching this video of some U.S. warplane breaking the sound barrier and there was this, sort of, vertical halo around the entire mid-section of the plane----a ring of smoke, so to speak. It looked really cool. What the hell was that?!

UB, Phy101: Chapter 14, Pg 2

Physics 101: Physics 101: Chapter Chapter 14 14Ideal Gas Law & Kinetic TheoryIdeal Gas Law & Kinetic Theory

Today’s lecture will cover Textbook Chapter 14.1-14.2

UB, Phy101: Chapter 14, Pg 3

Aside: The Periodic TableAside: The Periodic Table

UB, Phy101: Chapter 14, Pg 4

The Periodic Table Explained ?The Periodic Table Explained ?

proton

neutron

electron

Look carefully

UB, Phy101: Chapter 14, Pg 5

Energy vs Mass (more in Physics Energy vs Mass (more in Physics 102)102)

He (m=4.0026 u) O (M=15.9995 u)

4 x He = 16.01 u

Mass difference = 0.01 u = binding energy

So energy is the same as mass somehow ??

E = mc2

UB, Phy101: Chapter 14, Pg 6

Atoms, Molecules, and MolesAtoms, Molecules, and Moles

1 mole = 6.022 x 1023 molecule (NA = Avogadro’s Number)

1 = 1 atomic mass unit = (mass of 12C atom)/12» approximately #neutrons + #protons» atomic weight W

Mass of 1 mole of “stuff” in grams = molecular mass in

e.g., 1 mole of N2 has mass of 2x14=28 grams

UB, Phy101: Chapter 14, Pg 7

Back to Physics 101: Chapter 14, Back to Physics 101: Chapter 14, Preflight Preflight

Which contains the most molecules ?

1. A mole of water (H2O)

2. A mole of oxygen gas (O2)

3. Same

H2O

O2

correct

UB, Phy101: Chapter 14, Pg 8

Chapter 14, Preflight Chapter 14, Preflight

Which contains the most atoms ?

1. A mole of water (H2O)

2. A mole of oxygen gas (O2)

3. Same

H2O (3 atoms)

O2 (2 atoms)

correct

UB, Phy101: Chapter 14, Pg 9

Chapter 14, Preflight Chapter 14, Preflight

Which weighs the most ?

1. A mole of water (H2O)

2. A mole of oxygen gas (O2)

3. Same

H2O (M = 16 + 1 + 1)

O2 (M = 16 + 16)

correct

UB, Phy101: Chapter 14, Pg 10

The Ideal Gas LawThe Ideal Gas Law

pV = NkBT

p = pressure in N/m2 (or Pascals)V = volume in m3

N = number of moleculesT = absolute temperature (K)k B = Boltzmann’s constant

» kB = 1.38 x 10-23 J/K» note: pV has units of N-m or J (energy!)

UB, Phy101: Chapter 14, Pg 11

UB, Phy101: Chapter 14, Pg 12

The Ideal Gas LawThe Ideal Gas Law

pV = NkBT Alternate way to write this

N = number of moles (n) x NA molecules/molepV= NkBT

» nNAkB T

» n(NAkB)T» nRT

pV = nRTR = ideal gas constant = NAkB = 8.31 J/(mol-K)

UB, Phy101: Chapter 14, Pg 13

The Ideal Gas LawThe Ideal Gas Law

pV = nRT

R = ideal gas constant = NAkB = 8.31 J/mol/K

Other units: R = .0823 l-atm/mol/K R = 1.99 cal/mol/K

UB, Phy101: Chapter 14, Pg 14

Ideal Gas Law: ApplicationsIdeal Gas Law: ApplicationspV = nRTpV = nRT

When T is constant, pV is constant (Boyle’s Law)Isothermal process demo

When p is constant, V is proportional to TIsobaric process demoHot air balloon, helium and oxygen in LN2

When V is constant, p is proportional to TIsohoric process demoOpen tube manometer

UB, Phy101: Chapter 14, Pg 15

Chapter 14,Chapter 14, Preflight Preflight In terms of the ideal gas law, explain briefly how a hot air balloon works.

now we now that hot air rises. so therefore the bolloon collects all the hot air until it over comes the weight of the basket below and you have lift off

Note! this is not a pressure effect, it is a volume effect. As T increases, volume increase, so that density decreases the balloon then floats due to Archimedes principle. The pressure remains constant!

Charles Law. As a gas is heated, it expands. When the air in the balloon expands, its density goes down. Thus, it is less dense than surrounding air and "floats"

Hot air, being less dense than cold air, can lift the balloon.

For a gas with a constant molecular weight, the pressure is proportional to the product of the density and the temperature. Less molecules of hot air are needed compared to cold air to achieve the same pressure. The density of hot air is less than that of cold air, which allows the ballon to float.

UB, Phy101: Chapter 14, Pg 16

UB, Phy101: Chapter 14, Pg 17

Kinetic Theory:Kinetic Theory:The relationship between energy and temperatureThe relationship between energy and temperature

(for monatomic ideal gas)(for monatomic ideal gas)

m

T3k v v B2

rms

nRT2

3 Tk

2

3 N KEN Uenergy internal B

Tk2

3 vm

2

1 KE B

2 Per moleculeDEMO

UB, Phy101: Chapter 14, Pg 18

Chapter 14, Preflight Chapter 14, Preflight

Suppose you want the rms (root-mean-square) speed of molecules in a sample of gas to double. By what factor should you increase the temperature of the gas? 1. 2 2. 3. 4

2correct

Tk2

3 vm

2

1B

2 KE

• If v doubles, v2 quadruples

• Therefore, T quadruples