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Derive the relationship between density and pressure. |
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Answer» 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. |
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