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**THERMAL PHYSICS**

**The Gas Laws**

Boyle's law |
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__Boyle's Law__

**For a fixed mass of gas at constant temperature and pressure, the pressure is inversely proportional to the volume. **

making the proportionality into an equality,

where ** k** is a constant

Now, consider a fixed mass of gas at one temperature at different pressures and volumes,

elimenating the constant **k**

__Charles' Law__

**For a fixed mass of gas at constant temperature and pressure, the volume is directly proportional to the temperature(K). **

making the proportionality into an equality,

where ** m** is a constant

Now, consider a fixed mass of gas at one pressure at two different temperatures and volumes,

elimenating the constant * m*,

__Pressure Law__

**For a fixed mass of gas at constant temperature and pressure, the pressure is directly proportional to the temperature(K). **

making the proportionality into an equality,

where * n* is a constant

Now, consider a fixed mass of gas at one volume at two different temperatures and pressures,

elimenating the constant* n*,

__Combined Gas Equation__

The three gas law equations, with constants *k **,** m **,*** n** are :

These can be combined into one equation:

where * K* (upper case) is a new constant

Now, consider a fixed mass of gas at two different temperatures, volumes and pressures,

elimenating the constant* K*,

__The Mole__(mol)

**A Mole is the amount of substance that has the same no. of particles as there are atoms in 12g of carbon 12. **

or

**A Mole of anything contains the Avagadro number of particles. **

Avagadro's Number (**N _{A}**) = 6.022 x 10

^{23}mol

^{-1}

A Mole is a very large number.

Consider the Earth's population at present 6 x 10^{9}. A Mole of people would be equivalent to 10^{14} Earths !

The **mass** of one mole of a substance is the relative molecular mass(**RMM**) of a substance expressed in grams.

eg 1 mole of molecular hydrogen (H_{2}) has a mass of 2g

__The Ideal Gas Equation__

The combined gas equation,

can be modified to take account of the amount of gas in units of moles.

This is done by making the constant * K* a function of the number of moles

**n**of gas present .

**R** is the **Universal Gas Constant** (= 8.31 JK^{-1}mol^{-1} )

The '**equation of state**' for an ideal gas is then given by:

An '**ideal gas**' is not a perfect model, but it is a good approximation.

The concept is based on the assumption that gas internal energy is** only kinetic in nature**.

The equation is accurate for **real gases at low pressures** and at **temperatures well above liquefaction**.

__Units__

* V* - volume

**cubic metres**

**m**

^{3}

* p* - pressure

**Pascals**

**Pa**(1

**Pa**= 1

**Newton per square metre**)

* T* - temperature

**Kelvin K**

**NB** The symbol** p** is lower case. Momentum also uses this symbol.

Capital * P* is the symbol for Power.

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