Boyle’s Law Relation With Kinetic Theory And Ideal Gases

Use the expression for pressure in the kinetic theory of gases to derive Boyle’s law at a constant temperature.

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Complete step-by-step solution -

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The pressure exerted by a gas according to kinetic theory of gases is, P=1/3*ρv2

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ρ is the density and v is the root mean square velocity of the gas molecules

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PV = 1/3Mv2 = 2/3Ek where Ek is the kinetic energy of the gas

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At a constant temperature, the velocity will be constant and hence the kinetic energy will be constant.

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PV = constant

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Thus, at a constant temperature, the pressure of a gas is inversely proportional to the volume occupied by it. This is Boyle’s law.

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