Gas Laws
Boyle's law
When the state of a gas is changed (by squeezing into a smaller volume for example) the gas responds in a simple way.
Boyle's law is a relationship concerning the compression and expansion of a gas at constant temperature.
This empirical relationship formulated by Robert Boyle in 1662 states that the pressure (P) of a given quantity of gas varies inversely with its volume (V) at constant temperature (T).
PV = constant (if T is constant)
Charles Law
The volume occupied by a fixed amount of gas is directly proportional to its temperature, if the pressure remains constant.
That is to say that for the pressure to remain the same a fixed mass of gas must become hotter to occupy a larger volume and cooler to occupy a smaller volume.
In a similar way if the volume remains constant, a fixed volume of gas will need to get hotter for the pressure to increase and cooler for the pressure to decrease.
VT^{-1} = constant (if P is constant)
PT^{-1} = constant (if V is constant)
Absolute Temperature
When discussing vacuum and the Gas Laws we always refer to temperature in absolute terms.
Absolute zero is the lowest temperature theoretically possible and is approximately -273°C or zero degrees on the Kelvin scale (K).
The concept of absolute zero is derived from the Gas Laws.
When a plot of experimental values of pressure versus temperature is extended back the value for absolute zero is the temperature at which the pressure is zero.
In reality this never occurs, as the gas will liquefy before it reaches this temperature.
Combined Gas Laws
A perfect gas is a gas that conforms, in physical behaviour to a particular idealised relationship between pressure, volume and temperature called the general gas laws as described earlier.
This law is a generalisation containing both Boyles law and Charles law and states for a specified quantity of gas the product of the volume (V) and pressure (P) is proportional the absolute temperature.
PVT^{-1} = constant
P_{1}V_{1}T_{1}^{-1} = P_{2}V_{2}T_{2}^{-1} or PV = kT where k = constant
Note: For most vacuum calculations the perfect gas laws can be assumed. This is not true at pressures above atmospheric pressure.
Avogadro's Law & the mole
The mole is a SI unit and is defined as the amount of a substance that contains the same number of molecules. The number was determined experimentally and was based upon the number of atoms in 12g of carbon-12. Carbon-12 was chosen arbitrarily serve as the reference standard for the SI mole unit.
The number of units per mole is very large and is called Avogadro’s number. The number is 6.0221367 x 10^{23} i.e. 602,213,670,000,000,000,000,000.
Avogadro’s law states that under the same conditions of temperature and pressure, equal volumes of gas contains an equal number of molecules.
The volume occupied by one mole of gas is 22.4 liters at standard temperature and pressure (1013 mbar and 0°C) and is the same for all gases according to Avogadro's Law.
If the temperature, pressure or volume is different then the number of moles can be calculated using the Ideal Gas Equation.
Molecular weights of some common gases
Universal Gas Constant
This is a fundamental physical constant. As previously discussed the pressure multiplied by its volume and divided by its temperature is constant for a given mass of gas. When one of these three is altered at least one of the others has to change for this expression to remain constant. This is constant for all gases and provided the mass being compared is 1 mole then:-
PVT^{-1} = R
The Universal Gas Constant is the amount of energy required to raise one mole of gas by one degree in temperature and is given as energy per degree per mole.
Universal Gas Constant = Ŕ = 8.3 Joules per degree Kelvin per mole
PVT-1 = Ŕ
P (Atmospheric pressure) = 1013 bar = 1.013 x 10^{5} Pa
V (Molar volume) = 22.4l = 22.4 x 10^{-3} m^{3}
T (Temperature) = 0°C = 273K
Then PV/T = 1.013 x 10^{5} x 22.4 x 10^{-3} / 273 = 8.3 Joules per degree Kelvin per mole
Ideal Gas Equation
If we know the quantity of a gas (i.e. the number of moles) then the following equation is obeyed and is known as the Ideal Gas Equation
PV = nŔT (Pressure x volume = number of moles x universal gas constant x temperature)
From this equation you can equate the total amount of energy that a gas possesses for a given quantity of gas.
Another equation you may be familiar with which is essentially the same but dealing with a given mass of a gas rather than the number of moles of a gas is:-
PV = mRT
Where
R = relative gas constant for a particular gas (found in steam tables, etc)
m = the mass of the gas.
For Air R = 0.2871 kJ.kg-1.K-1
For Water Vapour R = 0.4615 kJ.kg-1.K-1
Summary
Boyles Law
States that pressure and volume of a gas are inversely proportional with constant temperature.
Charles Law
States that temperature and volume are directly proportional with constant pressure.
Combined Law
States that the product of pressure and volume divided by the absolute temperature will be constant.
Avogadro's Law
6.0221367 x 1023 is the number of molecules of a gas at standard temperature and pressure in a 22.4 liter volume.
Universal Gas Constant
8.314 J K-1 mole-1 is the amount of energy required to raise one mole of gas by one degree in temperature.
Ideal Gas Equation
PV = nRT the equation that equates the energy possessed by a given quantity of gas. |