kinetic theory of gases physics 102 professor lee carkner lecture 3 (session: 104884) would anyone...
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Kinetic Theory of Gases
Physics 102Professor Lee
CarknerLecture 3
(Session: 104884)
Would anyone in Monday 2:30 lab or Tuesday 12:30 lab like to switch to another lab?
(See me)
Thanks!
PAL: Quenching a Dagger Suppose a silver dagger of mass ms at Ts is
immersed in a mass mw of water at Tw. What is the final temperature of the water?
Qsilver + Qwater = 0
csmsT + cwmwT = 0
csms(Tf-Ti) + cwmw(Tf-Ti) = 0
csms(Tf - Ts) + cwmw(Tf- Tw) = 0
csmsTf -csms Ts + cwmwTf - cwmw Tw = 0
csmsTf + cwmwTf = csms Ts + cwmw Tw
(csms+ cwmw)Tf = csms Ts + cwmw Tw
Tf = (csms Ts + cwmwTw)/(csms+ cwmw)
Gases 1 mole = 6.022 X 1023 molecules
6.022 X 1023 = Avogadro’s Number = NA
Three variables: m = M = molar mass =NAm n =
Why do we care about moles?
Can do experiments to find relationships between P, V, T and n Such relationship called equation of state
Ideal Gas
At low density they all reduce to ideal gas lawPV = nRT
Ideal gas pretty good approximation to most real gases
Can also write as:
Where N is number of molecules and k in the Boltzmann constant = 1.38 X 10-23 J/K
Other Laws Boyle’s Law
If n is fixed and T is constant:
PV = constant If V goes up, P goes down Called an isothermal
process Charles’s Law
If n is fixed and P is constant:
V/T = constant If T goes up, V goes up Called an isobaric
process
Gay-Lussac’s Law If n is fixed and V
is constantT/P = constant
If T goes up, P goes up
Called an isochoric process
Using the Ideal Gas Law If you know three of P,V,n and T, you
can solve for the fourth
PiVi/Ti = PfVf/Tf for any process
Whenever you see P, V, T, think ideal gas law
Ideal Gas Law Units SI units:
P is Pascals (Pa) 1 Pa = 1 kPa = 1000 Pa 1 atmosphere =
V in cubic meters (m3)
T in Kelvin (K)
You must use Pa, m3 and K (if you use R = 8.31)! Don’t use atm or liters!
What is Temperature? Need to understand the microscopic properties to
understand the macroscopic properties If you change the temperature you change the ways
in which the molecules move
How do the moving molecules produce a pressure?
From our knowledge of force and momentum (Ch. 4 and 7) we can say:
Lots of molecules with lots of energy produce lots of force
Temperature and Energy
KE = (1/2) m v2rms
High T = large KE = large velocity
Temperature is a measure of the average kinetic energy of the
molecules
So we use the root-mean-squared velocity, vrms A sort of average velocity
Relations We can derive:
KE = (1/2) mv2rms = (3/2)kT
KE = m = mass of molecule vrms = k = Boltzmann constant = 1.38 X 10-23 J/K
For a given gas, m and k are constant so: T KE v2
rms
Note: KE = 0 only at absolute zero
Velocities
but not all molecules have the same velocity
Molecules are constantly colliding Sometimes speeding up
While a given molecule can have any velocity, some velocities are more probable than others Velocities follow the Maxwellian probability distribution
Maxwell’sDistribution
Planetary Atmospheres
Why do some planets have atmospheres and others do not?
In order to have an atmosphere:vescape > 5vrms
(2GMplanet/Rplanet) > 5(3kT/mmolecule) What properties are conducive to
retaining an atmosphere?
Next Time Read: 13.12, 14.5 Homework: Ch 14, P: 21, 23, Ch 13, P:
33, 55
A certain amount of heat Q is applied to a 1 gram sample of 3 different materials, producing a different temperature increase T in each. Which has the greatest specific heat?
a) Material A: T = 1 Cb) Material B: T = 2 Cc) Material C: T = 3 Cd) All have the same specific heate) We can’t tell from the information
given
Through which material will there be the most heat transfer via conduction?
a) solid ironb) woodc) liquid waterd) aire) vacuum
Through which 2 materials will there be the most heat transfer via convection?
a) solid iron and woodb) wood and liquid waterc) liquid water and aird) vacuum and solid irone) vacuum and air
Through which 2 materials will there be the most heat transfer via radiation?
a) solid iron and woodb) wood and liquid waterc) liquid water and aird) vacuum and solid irone) vacuum and air
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