# prove that PV=1/3 mNc2

### (i) Boyle's law

We have PV =1/3 [mNc2] but c2 is proportional to the absolute temperature T.

For a given mass of gas at constant temperature 1/3 [mNc2] is constant and therefore PV is constant and this is Boyle's law.

The Ideal Gas equation for n moles of gas is PV = nRT and so for one mole of gas we have PV = RT, where R is the gas constant. But in one mole of gas there are L molecules where L is the Avogadro constant (6.02x1023) and therefore:

PV = (1/3)[mLc2] = RT

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