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THERMAL PHYSICS

 

The Gas Laws

 

Boyle's law

Charles' law

Pressure law

combined gas equation

Mole

ideal gas equation

units

 

 

 

Boyle's Law

 

 

Boyle's Law graph

 

 

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

 

pressure inversely proportional to volume

 

making the proportionality into an equality,

 

pressure times volume equals a constant

 

where k is a constant

 

 

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

 

pressure and volume for different circumstances

 

elimenating the constant k

 

Boyle's law for two sets of circumstances

 

 

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Charles' Law

 

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

 

 

Charles' Law graph

 

 

 

Charles' Law proportionality

 

making the proportionality into an equality,

 

Charles' Law equation

 

where m is a constant

 

volume divided by temperature equals a constant

 

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

 

different values of volume and temperature

 

elimenating the constant m,

 

Charles' law for different volumes and temperatures

 

 

 

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Pressure Law

 

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

 

 

Pressure law graph

 

 

pressure proportional to temperature

 

making the proportionality into an equality,

 

pressure temperature equation

 

where n is a constant

 

pressure divided by temperature equal to a constant

 

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

 

different values of pressure and temperature

 

elimenating the constant n,

 

pressure equation for two values of pressure and temperature

 

 

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Combined Gas Equation

 

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

 

pressure times volume equals a constant        volume divided by temperature equals a constant        pressure divided by temperature equal to a constant

 

These can be combined into one equation:

 

comined gas equation #1

 

where K (upper case) is a new constant

 

 

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

 

p, V and T for a fixed mass of gas

 

elimenating the constant K,

 

comined gas equation

 

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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 (NA) = 6.022 x 1023 mol-1

 

A Mole is a very large number.


Consider the Earth's population at present 6 x 109. A Mole of people would be equivalent to 1014 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 (H2) has a mass of 2g

 

 

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The Ideal Gas Equation

 

The combined gas equation,

 

comined gas equation #1

 

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 .

 

ideal gas equation constant

 

R is the Universal Gas Constant (= 8.31 JK-1mol-1 )

 

 

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

 

the Ideal Gas Equation

 

 

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.

 

 

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Units

 

V - volume cubic metres m3

 

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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