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