# S-Cool Revision Summary

## S-Cool Revision Summary

#### Thermometric properties

To measure the temperature of an object you first need to find something that varies with temperature. This is called a **Thermometric property.**

For example, the volume of mercury, the resistance of a piece of wire and the pressure of a gas in a fixed volume.

#### The Centigrade scale

**To measure the temperature of an object:**

- Measure the changes to a thermometric property of a substance in thermal equilibrium with the object.
- Find the value of the thermometric property when it is at two known temperatures, called
**Fixed Points**e.g. the ice point and the steam point. - Assume that the thermometric property varies in a linear (straight line) way with temperature and you've got a centigrade scale.
- Use this equation to calculate the temperature, t, in the centigrade scale:

*Where:*

t = temperature

X_{t} = the thermometric property at unknown temperature t

X_{0} = the thermometric property at the ice point

X_{100} = the thermometric property at the steam point.

#### Absolute or Thermodynamic Temperature Scale

This is also known as the **Absolute Scale** or even the **Kelvin Scale** of temperature.

**Always** use thermodynamic temperatures when doing calculations involving temperature.

It is an imaginary, perfect temperature scale that has two fixed points - absolute zero and the triple point of water.

Temperatures are measured in Kelvin, K. 1K ≡ 1°C

#### The Celsius Scale

The thermodynamic scale is not used everyday because the numbers are too difficult. For example, water freezes at 273.15K.

The Celsius scale is exactly the same as the thermodynamic scale except that the freezing point of water is called zero degrees Celsius.

**Temperature in Celsius = Temperature in Kelvin - 273.15**

*Remember:* in calculations, always use the kelvin value.

#### Internal Energy

**Internal energy of a body has two components:**

**kinetic**(i.e. vibration, rotation and translation)**potential**(as a result of forces between particles -atoms or molecules)

There are only two ways that you can change the internal energy of a body

- Heat it (or cool it)
- Squash it (compress or expand it)

Hence the **First Law of Thermodynamics.**

"The increase in internal energy of a body (ΔU) is equal to the sum of the heat flowing **into** the body (ΔQ) and the work done by the body (ΔW)."

or

ΔU = ΔQ - ΔW

and

ΔW= pΔV

#### Specific Heat Capacity

**The definition of Specific Heat Capacity is:**

"The amount of energy required to raise the temperature of 1 kg (a unit mass) of the substance by 1°C (a unit temperature rise)"

*Symbol:*** c **

*Unit:*** Jkg ^{-1}K^{-1}**

*Where:*

ΔQ is the heat energy added (or removed)

m is the mass of the substance you are heating (or cooling)

Δθ is the change in temperature.

#### Specific Latent Heat

It takes a certain amount of energy to change the state of 1kg of water from solid to liquid. This amount of energy is called the **Specific Latent Heat**, l_{f}, of water

*The definition:*

"The amount of energy per kg (unit mass) required to change ice to water."

**Units:** Jkg^{-1}

*Where:*

ΔQ is the heat energy added

m is the mass of the substance involved.

There is no temperature term involved in this equation as it all takes place at the same temperature.

*Note:* that there are two occasions when you change state and both of these require different amounts of energy (as different things are happening to the atoms during the state changes). So there are two symbols.

*l*_{f} - latent heat of fusion - solid to liquid and back.

*l*_{v} - latent heat of vaporisation - liquid to gas and back.

#### Equations

c = ΔQ/mΔT | pV = nRT |

I = ΔQ/m | pV = N k T |

ΔU = ΔQ - ΔW | |

ΔW = 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} |