Thermal 2 Flashcards
What is Boyle’s Law?
for a fixed mass of gas, at a constant temperature, the pressure of a gas is inversely proportional to its volume
What is the Pressure Law?
for a fixed mass of gas, at constant volume, the pressure is directly proportional to the absolute temperature
What is Charles’ Law?
at constant pressure, the volume of a gas is directly proportional to its absolute temperature
What is the ideal gas equation? (Given in formula booklet)
pV = nRT or pV = NkT
What does “n” represent in the ideal gas equation?
the number of moles
What is meant by absolute zero?
the temperature where an ideal gas has zero volume and exerts zero pressure, this is because molecular KE = 0
What is meant by Brownian motion?
particles suspended in a medium follow a random walk
What is meant by a random walk?
particles move in straight lines, of random length and in random directions
What is Brownian motion of (for example smoke) particles due to?
due to collision with very small air molecules
What does “N” represent in the ideal gas equation?
the number of molecules
What is meant by the molar mass of a substance?
the mass of 6 x 10^23 particles, Mr
How can you find the number of moles in the substance if you have its mass, and the molar mass?
n = mass of substance / molar mass
What is meant by one mole of a substance?
1 mole of a substance is the quantity of that substance that contains 6 x 10 ^23 particles
How can you find the number of molecules in a substance if you have its mass and molar mass?
N = (Avogadro constant) x (mass of substance)/(molar mass)
What are the 8 ideal gas assumptions?
- all molecules of a gas are identical
- the gas contains a large number of molecules
- the molecules have negligible volume compared with the volume of the gas
- the molecules move in random motion (direction and speed)
- attraction between molecules is negligible
- collisions between a molecule and another molecule/wall are elastic
- the molecules move in a straight line between collisions
- the forces acting during collisions act for a short time relative to the time between collisions
How do we use the assumption that all molecules of a gas are identical?
means the momentum change experienced by the molecules will be the same
How do we use the assumption that the gas contains a large number of molecules?
we can apply stats, take average
How do we use the assumption that molecules have negligible volume compared with the volume of the gas?
- means there is large spacing between gas molecules
- (also means the attraction between molecules in negligible as F ∝ 1/r^2)
What is meant by molecules moving in random motion?
moving in a random direction and moving with random speed
How do we use the assumption that molecules move in random motion?
motion in x, y, and z directions is equal (on average)
How do we use the assumption that the attraction between molecules is negligible?
- PE = 0 for ideal gas molecules
- internal energy = ∑KE
How do we use the assumption that collisions between molecules are elastic?
means kinetic energy is conserved
Why is it we assume that molecules move in a straight line between collision?
as there is no “attractive” force, only force when molecules “collide”
Why is it we assume that the forces acting during collisions act for a short time relative to the time between collisions?
as there is large spacing between molecules
Explain Boyle’s Law (at the molecular level)
- the pressure of the gas increases when the volume reduces because:
- the molecules travel less distance between impacts
- so the impacts with the walls are more frequent
Explain the pressure law (at the molecular level)
- the pressure of a gas increases as the temperature rises because:
- the molecules have a greater average speed
- so the impacts with the walls are harder and more frequent
What is the relationship between the pressure a gas applies to the wall of its container, and the mean speed of the molecules?
the pressure a gas applies to the wall of its container is proportional to the mean square of the speed of the molecules
Explain why it is a squared relationship between the pressure of a gas and the mean speed of the molecules?
- when mean speed doubles:
- 2x rate of collision
- 2x momentum exchange per collision
What is the equation for the root mean square speed of the molecules?
Crms = √(((C1)^2 + (C2)^2 + …(CN)^2) / N)
Using pV = NkT and pV = (1/3)Nm(Crms)^2 show that the mean molecular KE = (3/2)kT
- KE = (1/2)(m)(Crms)^2
- (2/3)(KE)(N) = (1/3)(N)(m)(Crms)^2
- (2/3)(KE)(N) = pV
- (2/3)(KE)(N) = NkT
- (2/3)(KE) = kT
- KE = (3/2)kT
What does “m” represent in the equation pV = (1/3)Nm(Crms)^2 ?
the mass of 1 molecule
