Question

show that the pressure exerted by gas two third of the average kinetic energy per unit volume of the gas​

Answer 1

We know that the pressure exerted by a gas

P = ρv²/3

where,

ρ = density = mass/volume = M/V

and v = velocity

=> P = Mv²/3V..........eqn1

but we know that, kinetic energy = Mv²/2

=> 2KE = Mv²

putting this value in eqn above,

P = 2KE/3V

= 2/3 x (KE/V)

=> P = 2/3 x kinetic energy per unit volume of the gas​

Hence the pressure exerted by gas two third of the average kinetic energy per unit volume of the gas.

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