# S-Cool Revision Summary

## S-Cool Revision Summary

#### Kinetic Theory

Large numbers of particles moving in continuous random motion.

Evidence: Brownian motion, diffusion.

#### Assumptions

- large numbers

- elastic collisions

- no intermolecular forces

- negligible collision time

- negligible volume.

Note: ideal gases have no Ep component to their internal energy but... so...

p = 1/3ρ ⟨c2

#### Root mean square speed, rms speed

The speed term in the equation above is the average of the square speed which has a different value from the square of the average speed - do you see the difference? The root mean square speed is the square root of the mean square speed.

#### The Gas Laws

The three gas laws this ideal gas obeys perfectly are:

pV = constant (at constant temperature) constant (at constant volume) constant (at constant pressure)

Note: T stands for absolute temperature (in kelvin), not temperature in °C.

#### Boltzmann constant and Ek

The Boltzmann constant, k, is the universal molar gas constant for 1 atom or molecule.

Use it to derive:

1/2m ⟨c2⟩ = 3/2 NkT

This shows that the temperature of a gas sample depends only on the kinetic energy of the particles (atoms or molecules) that make it up.

#### Equations

 c = Q/mΔT pV = nrt l = Q/m p V = N k T ΔU = ΔQ - ΔW W = pΔV p = 1/3 ρ ⟨c 2 ⟩  #### Symbols

 c = specific heat capacity, Jkg-1K-1 U = internal energy, J lv = specific latent heat of vaporisation (liquid to gas and back), Jkg-1 Q = thermal energy, J lf = specific latent heat of fusion (solid to liquid and back), Jkg-1 W = work done, J Q = thermal energy, J ΔV = change in volume, m3 m = mass, kg p = pressure, Pa ΔT = change in temperature, K or °C T = temperature, K t = temperature, °C R = universal molar gas constant T = thermodynamic temperature, K n = number of moles Xt = value of thermometric property at temperature 't' N = number of molecules Xo = value of thermometric property at the ice point, 0°C k = Boltzmann constant X100 = value of thermometric property at the steam point, 100°C ρ = density, kgm-3 ⟨c 2⟩ = mean square speed, ms-1 