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Physics 101: Lecture 29 Ideal Gas Law

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Title: Physics 101: Lecture 29 Ideal Gas Law


1
Physics 101 Lecture 29Ideal Gas Law Kinetic
Theory
  • Todays lecture will cover Textbook Chapter 14

2
Fundamental building blocks of matter ?
  • Molecules are formed from atoms, held together by
  • the electromagnetic force.
  • Atoms consist of a positively charged nucleus and
    electrons, held together by the electromagnetic
    force.
  • The nucleus is formed from protons and neutrons,
    held together
  • by the strong force.
  • Protons and neutrons are formed from up and down
    quarks
  • (p uud, n ddu), held together by the strong
    force.
  • State-of-the art http//particleadventure.org/par
    ticleadventure
  • http//www.aps.org/units/dpf/quarks_unbound
  • 12 fundamental matter particles (12
    anti-matter particles)
  • six quarks and six leptons (e.g.,
    electron)
  • 4 fundamental forces (interactions)
  • electromagnetic (exchange of photon)
  • weak (exchange of W and Z bosons) b
    decay (sun)
  • strong (exchange of gluon) and
    gravity (exchange of graviton ?)

3
The Periodic Table
Mendelejew and Meyer (1869)
4
The Periodic Table
proton
neutron
electron
Atomic number 1 Atom H Atomic
mass 1.00797 u 1 u 1 atomic mass unit
(mass of 12C atom)/12 approximately neutrons
protons
5
Energy vs Mass
He (m4.0026 u)
O (M15.9995 u)
energy is mass and vice versa
6
Molecules, Atoms and Moles
  • Avogadro (1776-1856) All gases at same pressure,
    volume
  • and temperature contain the same number of
    gas particles.
  • One mole of a substance contains as many
    particles as they are atoms in 12 g of C12, i.e.
    6.022 x 1023 atoms.
  • NA 6.022 x 1023 1/mol is Avogadros Number
  • number of moles number of
    particles/NA
  • n N/NA
  • and
  • number of moles mass (in
    gram)/mass per mole (g/mol)
  • Mass of 1 mol of a substance in grams molecular
    mass in u
  • e.g., 1 mol of N2 has mass of 2x1428 grams
  • mparticle mass per mole/N
  • conversion factor 1u 1.6605 x 10-27 kg

7
Concept Question
  • Which contains the most molecules ?
  • 1. 1 mol of water (H2O)
  • 2. 1 mol of oxygen gas (O2)
  • 3. Same

8
Concept Question
  • Which contains the most atoms ?
  • 1. A mol of water (H2O)
  • 2. A mol of oxygen gas (O2)
  • 3. Same

9
Concept Question
  • Which weighs the most ?
  • 1. 1 mol of water (H2O)
  • 2. 1 mol of oxygen gas (O2)
  • 3. Same

10
The Ideal Gas Law
  • Ideal gas low density gt the only interaction
    that occurs between gas particles (and
    surrounding walls) is elastic collision gt An
    ideal gas is highly compressible.
  • If V decreases P increases !
  • Boyle and Mariotte (1662,1667) found
    experimentally that
  • P V constant if Tconstant (and
    Nconst.)
  • Experiments also revealed that
  • P is proportional to T (V and N
    constant)
  • P is proportional to N (V and T is
    constant)
  • gt P V is proportional to N T !

11
The Ideal Gas Law
  • P V N kB T
  • P pressure in N/m2 (or Pascals)
  • V volume in m3
  • N number of molecules
  • T absolute temperature (K)
  • k B Boltzmanns constant
  • kB 1.38 x 10-23 J/K
  • note pV has units of N m or J (energy!)

12
The Ideal Gas Law
  • P V N kB T
  • kB is Boltzmanns constant kB 1.38 x 10-23 J/K
  • Alternate way to write this
  • N number of moles (n) x NA molecules/mole
  • P V N kB T
  • n NA kB T
  • n (NAkB)T
  • n R T
  • P V n R T
  • R ideal gas constant NAkB 8.31 J/(mol K)

13
Kinetic TheoryThe relationship between energy
and temperature(for monatomic ideal gas)
Per molecule
14
Concept Question
  • 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
  • If v doubles, v2 quadruples
  • Therefore, T quadruples
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