gases

what makes gases different to liquids and solids?

they can be compressed

what is boyle’s law?

pressure is inversely proportional to volume

P ∝ 1 / V

what does adiabatic mean?

closed system, so no energy is being transferred from or to the surroundings

what is charles’ law?

volume ∝ temperature

what is the pressure / gay-lussac law?

P ∝ T

what is an ideal gas?

one that obeys boyle’s law perfectly

what is a perfect gas?

one that almost obeys boyle’s law perfectly, and therefore can still be used in equations

which temperature scale is used in gas laws and why?

kelvin , because kelvin starts at the absolute zero whereas celsius is relative to whatever substance we’re considering

what is the temperature change in kelvin and celsius?

the same, +1K = +1C

volume and pressure

boyle’s law , P ∝ 1 / V

volume and temperature

charles’ law , V ∝ T

pressure and temperature

pressure / gay-lussac law , P ∝ T

ideal gas equation

p V = n R T

• p = pressure

• v = volume

• n = mol number

• R = gas constant, 8.31

• T = temperature

p V = N k T

• p = pressure

• v = volume

• N = number of molecules

• k = boltzmann constant , 1.38 × 10–2

• T = temperature

avogadro constant Na

1 mol = 6.02 × 10²³ molecules

ratios

P₁ V₁ / n₁ T₁ = P₂ V₂ / n₂ / T₂

explain P₁ V₁ / n₁ T₁ = P₂ V₂ / n₂ / T₂

p V = n R T , so R = P V / n T. since R is a constant, this means P V / n T is the same before and after, therefore P₁ V₁ / n₁ T₁ = P₂ V₂ / n₂ / T₂

what does isothermic mean?

temperature is constant

what does isobanic mean?

pressure is constant

is n constant?

usually, unless we’re letting gas out / in

what is brownian motion?

the random movement of particles in a fluid

what are the 5 assumptions we make about ideal or perfect gases?

• move with brownian motion

• no attractive forces between particles

• particle volume is negligible compared to container volume

• all collisions are elastic

• the duration of the collisions is negligible compared to the time between collisions

what is the time taken between the collision of a particle against a particular wall?

the time taken to travel two lengths of the container, as time between collisions is measured as opposed to collision time

what is the change of momentum for a particle colliding with a wall?

2 m u

collision force equation

F = 2 m u / (2 L U)

= m u² / L

where L is the length of the box it travels across

pressure equation

P = force x area

= m u² / L_y x L_x x L_z

= m u² / V

what is rms?

root mean square, where N = number of molecules

why do we use rms?

because the mean velocity of the particles is zero

why is the mean velocity of particles zero?

because they travel in all directions equally

what is c_rms ?

the combination of speeds in all three directions

what is u²_rms = ?

u²_rms = 1/3 c²_rms

what is u_rms = ?

u_rms = √ (u₁² + u₂² + u₃² + …) / N

why is 1/3 used?

because the particles can travel 3 ways , the length, the width, and the depth

what is the kinetic theory equation?

P V = 1/3 N m c²

• m = mass of 1 molecule

• N m = total mass of gas

• c = c_rms average speed of molecules

P = 1/3 p c²

• as N M / V = density

3 k T = m c²

• as p V = N k T and therefore N k T = 1/3 N m c²

E_k = 3/2 k T

• E_k = kinetic energy of 1 molecule

• from 3 k T = m c² halved

when is work done on a gas?

when it is compressed

when is a gas doing work?

when it expands

what is the work done on a p-v graph?

the area under the graph (count the squares) / line

• if isothermal (constant T), P₁V₁ = P₂V₂ (arrow going up the curve)

• if isobaric (constant P), V₁ / T₁ = V₂ / T₂ , work done = P Δ V (block under the graph)

• if at constant volume, P₁ / T₁ = P₂ / T₂ . it’s being cooled so no work done (arrow going straight down)