Kinetic Theory of Gasses Physics 102 Professor Lee Carkner Lecture 4

PAL #3 Heat  Q will warm 1 g of material A by 3 degrees C and 1 g of material B by 4 degrees C   Q is same, but  T smaller, so c is larger   Conduction   Virtually no conduction through air  Convection   Radiation 

What is Temperature?   A gas is a collection of lots of moving molecules   For example, if we increase T we increase P  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 = large KE =  Low T = small KE = 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 = root-mean-squared velocity  k = Boltzmann constant = 1.38 X 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?   Gas molecules are moving and may escape  In order to have an atmosphere: v escape > v rms  What properties are conducive to retaining an atmosphere?

Cassini Approaches Titan

Titan   Why does it have an atmosphere?  What type of gas might the atmosphere be made of?

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  Molecules are constantly colliding    While a given molecule can have any velocity, some velocities are more probable than others 

Maxwell  Thermalized molecules will have a Maxwellian velocity distribution   Probability tails off to high or low velocity   Can only determine bulk properties

Maxwell’s Distribution

Gases  m =  1 mole = X molecules  Avogadro’s Number = 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 gas  Can also write as:  Where N is number of molecules and k in the Boltzmann constant

Ideal Gas Law Units  SI units:  P is Pascals (Pa)  1 Pa =  1 kPa =  1 atmosphere =  V in cubic meters (m 3 )   T in Kelvin (K)  T K = T C

Other Laws  Boyle’s Law  If n is fixed and T is constant:  If V goes up, P goes down   Charles’s Law  If n is fixed and P is constant:  If T goes up, V goes up   Gay-Lussac’s Law  If n is fixed and V is constant  If T goes up, P goes up 

Using the Ideal Gas Law   For fixed amounts of gas, n is constant and we have relationship between P, V and T   nM is the mass of the gas so nM/V is the density 

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, 6-8 pm, 304 Science