# 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 E_{p} component to their internal energy

but...

so...

p = 1/3ρ ⟨c^{2}⟩

#### 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 E_{k}

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

**Use it to derive:**

1/2m ⟨c^{2}⟩ = 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^{-1}K^{-1} |
U = internal energy, J |

l_{v} = specific latent heat of vaporisation (liquid to gas and back), Jkg^{-1} |
Q = thermal energy, J |

l_{f} = specific latent heat of fusion (solid to liquid and back), Jkg^{-1} |
W = work done, J |

Q = thermal energy, J | ΔV = change in volume, m^{3} |

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 |

X_{t} = value of thermometric property at temperature 't' |
N = number of molecules |

X_{o} = value of thermometric property at the ice point, 0°C |
k = Boltzmann constant |

X_{100} = value of thermometric property at the steam point, 100°C |
ρ = density, kgm^{-3} |

⟨c ^{2}⟩ = mean square speed, ms^{-1} |