## Episode 602: Ideal gases and absolute zero

Lesson for 16-19

- Activity time 75 minutes
- Level Advanced

This episode establishes the ideal gas law, and how to use it. NB many texts use the terms ideal gas and perfect gas as meaning the same thing. Strictly speaking an ideal gas is one that obeys Boyle’s law with complete precision. A perfect gas is a real gas under conditions that Boyle’s law is a valid enough description of its behaviour.

Lesson Summary

- Discussion: The ideal gas law, moles and the Kelvin scale of temperature (30 minutes)
- Worked examples: Using the equation; temperature conversions (15 minutes)
- Student questions: Practice questions (30 minutes)

## Discussion: The ideal gas law, moles and the Kelvin scale of temperature

Both Charles’ law and the pressure law lead to an extrapolation back to zero volume or pressure which would imply the temperature scale can go no further. For all gases, that zero point (absolute zero) is (roughly) the same and although clearly the gas would no longer be a gas there, this is an important implication.

The separate laws can be combined into the ideal gas law,
*P**V* = N*R**T*. Make sure that your students understand the different symbols in this equation: N is the number of moles of gas and *R*
is the molar gas constant, i.e. the gas constant for one mole of substance, with the value 8.3 J^{K-1}.

It may be necessary to review these ideas. Many students will have learned that 1 mole of gas occupies 22.4 litre (at STP) or 24 litre (at RTP). It will be necessary to break them out of the habit of using this shortcut in order to apply the ideal gas law correctly. 1 mole is simply a standard number of atoms, Avogadro’s number, 6.023 × 10^{23}. The volume of one mole follows from the ideal gas law and the molar gas constant. They should also recall how to calculate the number of moles of a substance from

n = massrelative molecular mass.

The ideal gas law is approximately true for most gases, and as its name implies is exactly true for an ideal gas, an imaginary gas which obeys Boyle’s law perfectly.

Such a gas can be used to define the thermodynamic temperature scale with its zero where *P* and *V* drop to zero. In practice we know that there is a small amount of energy at absolute zero, the so-called zero-point motion of quantum mechanics. So it is best to define absolute zero as the point of lowest energy not zero energy.

To be strictly accurate, the Kelvin and Celsius scales coincide at the triple point of water, which is 0.01 ° C or 273.16 K, and so the conversion between the two scales is:

temperature in K = temperature in °C + 273.15.

The conventional symbols are:

*T*for thermodynamic (absolute) temperature, SI unit: kelvin, symbol K-
*q*for temperature in °C.

## Worked examples: Using the ideal gas law; temperature conversions

It is necessary to emphasise that the proportionality laws only apply with absolute temperature, so make sure that your students know when to work in K and how to convert between ° C and K.

Show a worked example or two of this.

Also, work through an example or two using the ideal gas law.

Episode 602-1: Ideal gases (Word, 20 KB)

## Student questions: Practice questions

Practice questions on gas laws, moles, absolute zero.

Episode 602-2: Using the ideal gas relationships (Word, 31 KB)