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how to derive boyles law formula. At very high temperatures and low pressures gases obey Charles law. V 1 is the initial volume occupied by the gas.
Equating the two we have dfracnalpha TPnbeta leftPrightT The number of moles n cancels. As we can see the ratio of the final and initial pressure is the inverse of the ratio for volumes. P 1 V 1 P 2 V 2.
P 2 20 50 1.
Rearranging gives dfracalpha TTPbeta P In this equation the left side is a function only of temperature the right side only of pressure. Boyles law states that for a fixed amount of gas at a constant temperature the volume of the gas is inversely proportional to the pressure of the gas. Later Joseph Gay-Lussac in 1802 modified and generalized the concept as Charless law. There are a couple of ways of expressing the law as an equation.