Class 11 Physics Kinetic Theory Perfect Gas Equation

Perfect Gas Equation

• Perfect gas equation is given by PV=μRT,
• WhereP,V are pressure, volume, T =absolute temperature,μ = number of moles and R =universal gas constant.
• R= kBNA where kB = Boltzmann constant and NA = Avogadro’s Number
• This equation tells about the behaviour of gas at a particular situation.
• If a gas satisfies this equation then the gas is known as Perfect gas or an ideal gas.

Different Forms of Perfect Gas Equation

1. PV=μRT (i)
• Where μ (no. of moles) = N/NA where N=no of molecules and NA = Avogadro number(no of molecules in 1 mole of gas).Orμ = M/Mowhere M=mass of sample of gas and Mo = molar mass.
• PV = (N/NA)RT(putting μ=N/NA in equation(i))
• By simplifying PV = NkBT
• PV=NkBT => P = (N/V) kBT => P=nkBT where n(number density) =N/V where N=number of molecules and V=volume.
• Therefore we get PV=nkBT
1. Substitute μ = M/Mo in equation(i)
• PV=(M/Mo) RT => P=(M/V)1/MoRT where
• ρ(mass density of the gas) = M/V
• Therefore P=ρRT/Mo

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