Question

Deduce Boyle’s law and Charle’s law from kinetic the theory of gases.

Answer 1

Boyle's law ⇒P∝1/V

Charle's law ⇒V ∝ T

according to kinetic theory of gases,

P = 1/3 M/V v_(rms)² .........(1)

since we know, Rms velocity is directly proportional to square root of temperature. so, v_(rms)² ∝ T

then, at constant temperature. v_(rms) remains constant.

so, P ∝ 1/V [ from equation (1), ]

⇒PV = constant.

means pressure of the given mass of the gas is inversely proportional to volume of gas. this law is known as Boyle's law.

again, when pressure of gas remains constant then, 1/3 M/V v_(rms)² = constant

or, V ∝ v_(rms)²

as we know, v_(rms)² ∝ T

then, V ∝ T

i.e., V/T = constant.

at constant temperature of a given mass of gas, volume is directly proportional to its temperature. this law is known as Charle's law.

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Answer 2

$\huge\bold\purple{Answer:-}$

Boyle's law states "Pressure of the given mass of a gas is inversely proportional to it's volume at constant temperatures." Charle's law states "Volume of the given mass of a gas is directly proportional to it's absolute temperature at a constant pressure."