Chapter 13/14 Flashcards
(26 cards)
Boyle’s Law
PV = k
Charle’s Law
V/T = k
Pressure Law
P/T = k
Ideal Gas Law (2)
pV = nRT
pV = NkT
equation of state
When does the ideal gas law work well?
Gases at low pressures and high temperatures.
Boltzmann’s constant
k = R/N(A)
Name 4 conditions of kinetic theory
- Particle velocity is proportional to pressure.
- faster particles, larger momentum, larger force on the wall. - Number of particles is proportional to pressure
- Volume of the box is inversely proportional to the pressure.
- Particles travel in random directions at different velocities.
Kinetic theory equation
pV = 1/3 NmC^2
Name a few assumptions of kinetic theory
- Gas contains large number of particles
- Particles move rapidly and randomly
- Motion of particles follow Newton’s laws
- Collisions are perfectly elastic.
- No other forces between particles.
- Forces during collisions are instantaneous.
- Particles have negligible volume compared to container.
Average distance moved of a particle in N steps
proportional to root N
What is specific heat capacity?
Amount of energy needed to raise the temperature of 1kg of the substance by 1K.
E = mc0
3 things about speed distribution of gas particles
As temperature of gas increases:
- Average particle speed increases
- Maximum particle speed increases
- Curve spreads out with same area.
What is internal energy?
Sum of kinetic and potential energy of particles within a system.
Relationship between Boltzmann’s constant and Molar gas constant
k = R/Na
Boltzmann’s constant can be thought of as the gas constant for one particle of gas in contrast to R as the gas constant for one mole of gas
How to find average KE of a gas molecule (ideal monatomic gas)
equate ideal gas equation with kinetic theory equation
nRT = 1/3 Nmc^2
Average distance moved by random walk with N steps
proportional to root N
What is the specific thermal capacity of a substance?
Amount of energy required to raise the temperature of 1kg of a substance by 1K.
J kg^-1 K^-1
Specific thermal capacity equation
ΔE = mcΔθ
What does the shape of the speed distribution of particles in a gas depend on?
Temperature of the gas.
As the temperature increases:
- Average particle speed increases
- Maximum particle speed increases
- Distribution becomes more spread out.
- Areas are equal
What is internal energy?
Sum of the kinetic and potential energy of the particles. (PE in the bonds which is 0 for ideal gases)
The amount of energy contained in a system.
1st Law of Thermodynamics
ΔU = Q + W
Change of internal energy = supply thermal energy + work done on it
Derivation of kinetic theory steps
- Change of momentum of gas molecule per collision with walls of box of length x = 2mv
- Time between collisions with wall = 2x/v (there and back)
- No of collisions per unit time = v/2x
- Force = change in momentum = change in momentum per collision x no of collisions per unit time
- F = 2mv x v/2x = mv^2/x
- For N particles, F = Nmv^2/x
- P = F/A = Nmv^2/Ax = Nmv^2/V
- Molecules all have different velocities so average is taken - mean square speed. PV = 1/3 Nmc^2 (force in only one dimension out of the 3)
What does a rise in absolute temperature result in?
Increase in kinetic energy of each particle and thus a rise in internal energy.
What is the boltzmann factor?
The ratio of the number of particles in energy states e joules apart.
Proportion of particles with activation energy.
