Relationship between density and pressure: With increase in pressure, gas molecules get closer and the density (d) of the gas increases. Hence, at constant temperature, pressure is directly proportional to the density of a fixed mass of gas.
From Boyle’s law,
PV = k1 …….(1)
∴ V = \(\frac{k_1}P\)
But, d = \(\frac{m}V\)
On substituting, V from equation (2),
d = \(\frac{m}{k_1}\) x P
∴ d = k P …….(3)
where k = New constant
∴ d ∝ P
Above equation shows that at constant temperature, the pressure is directly proportional to the density of a fixed mass of the gas.
