ch14 Flashcards
describe the motion of gas molecules
gas molecules move with constant brownian motion which is random motion of molecules caused by collisions with larger particles
how do gases exert a force (pressure) on it a container
the molecules continuously collide with each other and the walls of the container.
The collisions cause a change in momentum (impulse) which produces a force equal to the rate of change of momentum
this force gives pressure (P = F/A)
how do you get impulse from a force-time graph
impulse is equal to the area under a force-time graph
describe the pathing of particles
particles take a random path
they don’t travel in a straight line, but are constantly changing direction due to collisions, which is why diffusion is slow
equation for average distance moved (displacement)
distance moved = √N * step length (mean free step)
N = number of steps moved
step length = length of one step
boyle’s law
when gas is at a constant temperature, pressure P and volume V are inversely proportional
pV = constant
why does boyle’s law still work
as volume decreases, particles are closer together, increasing density and colliding more frequently
this exerts a greater force and therefore greater pressure on the container
1 bar = normal atmospheric pressure
the pressure in a car tyre is 2.6 bar
the tyre volume is 6 litres and the temp is constant
calculate the volume of gas that escapes if the tyre is punctured, assuming the tyre keeps its shape
pV = constant
first calculate constant
2.6 * 6 = 15.6 bar Litre
air will escape until the tyre pressure matches atmospheric pressure, 1 bar so work out volume after it’s expanded to that pressure
pV = 15.6 bar litre
V = 15.6 / P = 15.6 / 1
volume = 15.6 litres
but 6 litres remains constant in deflated tyre
volume escaping = 15.6 litre - 6 litre = 9.6 litre
how to calculate number of particles
number or particles = number of moles * Avogadro constant Na
how is pressure affected when the volume of a gas increases
when the volume of a gas increases, the space between molecules increases and so the time between collisions is larger
this cause the rate of collisions and so rate of change of momentum to decrease
this means the force exerted is lower, causing a decrease in pressure
what does Charles’ Law
at a constant pressure, volume V is directly proportional to absolute temperature T
number of moles =
number of moles =
mass of sample / mass of 1 mole
explain charles’ law
as temp increases, the average kinetic energy of the molecules increases
pressure is constant so the force and rate of change of momentum is constant
to keep it like this, the volume increases so the faster speed of molecules is compensated by the larger gaps between them
state pressure law
when a gas has a fixed volume, pressure is directly proportional to the absolute temperature
explain pressure law
as temperature increases, the average kinetic energy increases so speed of molecules increases
this increases the rate of collisions so producing a larger rate of change of momentum
this leads to a greater force exerted and so an increase in pressure
what does kinetic theory assume gases to be
ideal gases
assumptions of ideal gases
the gas contains a large number of molecules
the gas molecules are identical to each other
all collisions between molecules and container are perfectly elastic (energy is conserved)
time taken for collisions is negligible compared to time between collisions
there are no intermolecular forces so molecules do not attract each other
molecules are in constant random Brownian motion
gas particles obey Newton’s laws of motion
ideal gas equations:
pV = nRT
p = pressure (Pa) V = volume (m³) n = number of moles R = gas constant 8.314 J mol^-1 K^-1 T = temp in K
pV = NKT
N = number of molecules
K = boltzmann constant
1.38 * 10^-23 J K^-1
Boyle’s law relationship
pV = constant
charles’ Law relationship
V / T = constant
pressure law relationship
p / T = constant
how can you work out nR using Nk
Nk = nR N = number of molecules k = boltzmann constant n = number of moles R = gas constant
equation for force F caused by a single molecule on a wall
F = (mc²) / x F = force in newtons m = mass of molecule c = velocity x = length of box
final theoretical ideal gas equation
pV = 1/3 Nmc²
how do you get R.M.S, root mean square speed,
the average speed of molecules
you find the mean of the speeds squared
c² (small line over c)
derivation of 1/2mc(bar)² = 3/2kT
what does the equation tell us
we have 2 equations:
pV = 1/3 Nmc² and pV = NKT
mc² is very similar Ek = 1/2mv²
so pV = 1/3 Nmc² =
1/3N(1/2mc²) = but 1/3 * 1/2 doesn’t equal to 1/3, so we must have 2/3 and 1/2 to get the original 1/3
pV = 2/3N(1/2mc²) NKT = 2/3N(1/2mc²) KT = 2/3(1/2mc²) so:
3/2KT = 1/2mc²
for a mixture of gases like air the mean kinetic energy is the same at a given temperature
approximation of kinetic energy
3/2KT
3RT / 2Na
what is internal energy and how do you calculate it
internal energy is the amount of energy contained in a system
internal energy is the sum of kinetic and potential energies of its particles
internal energy in an ideal gas
there are assumed to be no intermolecular forces, so no potential energy
so assumption is internal energy = kinetic energy
equation of internal energy.
the first law of thermodynamics
ΔU = W + Q ΔU = change in internal energy Q = energy transferred thermally W = work done (energy) you calculate work done from W = force (N) * distance (m) W and Q can be negative
define specific heat (thermal) capacity
the energy needed to raise the temperature of a 1kg object by 1 degrees
equation for specific heat capacity
E (energy transferred) = ΔU (change in internal energy)
E = m c Δθ
E = energy (J) m = mass (KG) c = specific heat capacity θ = temperature (t)
equation for power, work done and time
power is the rate at which work is done
P = ΔU * t
P = power (W) ΔU = energy transferred t = time
