12.1
●
●
●
12.2
●
●
●
●
●
●
12.3
●
●
Atoms: smallest objects that still retain the chemical properties of a particular element
Molecule: a certain combination of atoms that bond together in a particular
arrangement
Ideal gas model
○ Assume that the average distance between the particles is much larger than
the size of the particles
○ Assume that the gas particles are point-like objects that only interact with
each other and with any surfaces in their containers during collisions
○ The particles do not attract each other at a distance the way they do in solids
and liquids
○ Between collisions, the particles move in straight lines at constant velocity
and only change their velocities during collisions
Pressure = force/area
Gauge pressure: the difference between the pressure in some container and the
atmospheric pressure outside the container
○ 1.0 atm = 1.0 * 10^5 Pa
Density = mass/volume
Mole = number of particles
Avogadro’s number = 6.02 * 10^23
○ The mass in grams of any substance that has exactly this many particles is
equal to the atomic mass listed in the periodic table of chemical elements
The mass of one mole of particles of any substance is called molar mass
○ Can use this to determine the mass of a single gas particle of any substance
by dividing the molar mass by avogadro’s number
○ m(particle) = m(mole)/N(a)
Assumptions:
○ The particles do not collide with each other
○ Assume that the collisions of particles with the walls are elastic
Use impulse-momentum ideas to analyze the collision
○ Before the collision, the particle has a positive x-component of velocity v(xi).
After the collision, the particle has a negative x-component of velocity v(xf)
○ mv(xi) + F(w on px)t(c) = mv(xf)
○
mv(xi) + (-F(p on wx)t) = -mv(xi) → speed is the same, newtons third law for
the force
○
○
○
12.4
●
●
= 2mv(xi) = F(p on wx)t
For the rest read the calculations on pg 362
Ends with equation: P=⅔ * (N/V) * (½ mv^2)
The number of particles in a container is determined by:
○ N = m(gas)/ m(molar mass) * N(a)
Assume the ratio PV/N is proportional to the absolute temperature of the gas
●
k(B) = 1.38 * 10^-23 J/K → Boltzmann’s constant
●
PV = Nk(B)T → T is temperature
○
●
●
●
We have to refer to the number of moles of the gas instead of number of
particles and hence N = nN(a) where n is the number of moles of the gas
○ PV = nN(a)k(B)T
■ N(a)k(B) is another constant called the universal gas constant R
○ PV = nRT
■ R = N(a)k(B) = 8.3
We can now connect the average kinetic energy of the gas particles to the absolute
temperature of the gas
○ K = 3/2 k(B)T
Temperature is an indication of not only the particle’s speed but also its kinetic
energy
If two different temperature gases are mixed, eventually the particles of the two
gases will have the same average kinetic energy and hence the same temperature →
thermal equilibrium
●
12.5
●
●
●
●
●
●
●
12.6
●
●
12.7
●
12.8
●
Using the average kinetic energy formula, we can find the root-mean-square speed
(rms speed)
○ K becomes 1/2mv^2 and then it just isolate v
Isothermal = temperature constant
Isobaric = pressure constant
Isochoric = volume constant
MEMORIZE THE TABLE IN YOUR NB REGARDING THE IDEAL GAS LAW
PROCESSES
Boyle’s law: PV = constant for constant temperature processes
Charles’s law: V/T= constant for constant pressure processes
Gay-Lussac’s law: P/T = constant
Maxwell distribution of molecular speeds
The ideal gas law describes gases accurately only over certain temperature and
pressure ranges
Problem-solving strategy
○ Decide if the system can be modeled as an ideal gas
○ Decide which macroscopic quantities remain constant and which do not
○ Construct a mathematical description– some version of the ideal gas law
○ Solve for the unknowns
Thermal energy
○ The sum of all the individual particles’ kinetic energies
●
●
○ U(th) = N(3/2 k(B)T)
How long can the Sun shine?
○ First need to determine how much thermal energy the Sun possesses
○ Then divide this amount of energy by the amount it loses every second from
the emission of visible light and radiation
○ Find the number of seconds the Sun can shine
○ N = m(sun)/m(hydrogen)
■ m(hydrogen) = M(molar mass hydrogen)/N(a)
○ The net gravitational force points toward the center of the Sun. The other
force in the system is the pressure force exerted by other particles on the
system
■ Sun is in equilibrium and is hence not expanding or collapsing
Diffusion: the process of molecules moving, due to their random motion from a region
of higher concentration to a region of lower concentration