Kinetic Theory of Gases
Physics 102
Professor Lee Carkner
Lecture 4
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
csmsDT + cwmwDT = 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)
A certain amount of heat Q is applied to a 1
gram sample of 3 different materials, producing
a different temperature increase DT in each.
Which has the greatest specific heat?
a) Material A: DT = 1 C
b) Material B: DT = 2 C
c) Material C: DT = 3 C
d) All have the same specific heat
e) We can’t tell from the information
given
Through which material will there be the most
heat transfer via conduction?
a)
b)
c)
d)
e)
solid iron
wood
liquid water
air
vacuum
Through which 2 materials will there be the
most heat transfer via convection?
a)
b)
c)
d)
e)
solid iron and wood
wood and liquid water
liquid water and air
vacuum and solid iron
vacuum and air
Through which 2 materials will there be the
most heat transfer via radiation?
a)
b)
c)
d)
e)
solid iron and wood
wood and liquid water
liquid water and air
vacuum and solid iron
vacuum and air
Gases
m =
1 mole = 6.022 X 1023 molecules
6.022 X 1023 = Avogadro’s Number = NA
M =
n = number of moles
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
Different gases have different equations of
state

PV = nRT
Where R is universal gas constant = 8.31
J/mol K

Can also write as:
Where N is number of molecules and k in the
Boltzmann constant = 1.38 X 10-23 J/K
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)
TK =
You must use Pa, m3 and K (if you use R = 8.31)!
Other Laws
 Boyle’s Law

Gay-Lussac’s Law

PV = constant
T/P = constant

 Called an isothermal
process
 Charles’s Law

V/T = constant

 Called an isobaric
process

Called an isochoric
process
Using the Ideal Gas Law

For fixed amounts of gas, n is constant
and we have relationship between P, V
and T

Whenever you see P, V, T, think ideal
gas law
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
If an increase in T increases P, then increasing
T must increase the KE of the molecules

High T =
Low T =
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:

Note: T must be in Kelvin

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?

Velocities
 A gas with a fixed value of T has a certain
average KE and velocity
but

 some molecules are moving slower or faster than
the mean

 Sometimes slowing down

 While a given molecule can have any velocity,
some velocities are more probable than others
 Velocities follow the Maxwellian probability
distribution
Maxwell’s
Distribution
Next Time
Read: 13.12, 14.5
Homework: Ch 14, P: 21, 23, Ch 13, P: 33, 55
Help Sessions start this week:
Tuesday and Thursday, 6-7 pm, 120 Science