Kinetic Theory of Gases Physics 102 Professor Lee Carkner Lecture 3 (Session: ) 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 m s at T s is immersed in a mass m w of water at T w. What is the final temperature of the water? Q silver + Q water = 0 c s m s  T + c w m w  T = 0 c s m s (T f -T i ) + c w m w (T f -T i ) = 0 c s m s (T f - T s ) + c w m w (T f - T w ) = 0 c s m s T f -c s m s T s + c w m w T f - c w m w T w = 0 c s m s T f + c w m w T f = c s m s T s + c w m w T w (c s m s + c w m w )T f = c s m s T s + c w m w T w T f = (c s m s T s + c w m w T w )/(c s m s + c w m w )

Gases   1 mole = X molecules  X = Avogadro’s Number = N A  Three variables:  m =  M = molar mass =N A m  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 law PV = 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 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 constant T/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   P i V i /T i = P f V f /T f 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 (m 3 )   T in Kelvin (K)   You must use Pa, m 3 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 v 2 rms  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, v rms  A sort of average velocity

Relations  We can derive: KE = (1/2) mv 2 rms = (3/2)kT  KE =  m = mass of molecule  v rms =  k = Boltzmann constant = 1.38 X J/K  For a given gas, m and k are constant so:  T  KE  v 2 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’s Distribution

Planetary Atmospheres  Why do some planets have atmospheres and others do not?    In order to have an atmosphere: v escape > 5v rms (2GM planet /R planet ) > 5(3kT/m molecule )  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 C b) Material B:  T = 2 C c) Material C:  T = 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) solid iron b) wood c) liquid water d) air e) vacuum

Through which 2 materials will there be the most heat transfer via convection? a) solid iron and wood b) wood and liquid water c) liquid water and air d) vacuum and solid iron e) vacuum and air

Through which 2 materials will there be the most heat transfer via radiation? a) solid iron and wood b) wood and liquid water c) liquid water and air d) vacuum and solid iron e) vacuum and air