Question

one mole of a gas at NTP is suddenly expanded to 4 times it's initial volume.If cv=2R .find the final pressure.​

Answer 1

Given,

one mole of a gas at NTP is suddenly expanded to 4 times its initial volume.

To find,

final pressure of gas.

Let initial volume is V,

initial pressure is P.

final volume of gas = 4V

given molar heat capacity at constant volume , Cv = 2R

but Cv = R/(γ - 1) = 2R

⇒γ = 1.5

as gas is suddenly expanded, it means process is adiabatic.

so use formula, PV^γ = constant.

⇒P₁V₁^γ = P₂V₂^γ

⇒PV^γ = P₂(4V)^γ

⇒PV^1.5 = P₂(4V)^1.5

⇒P(1/4)^1.5 = P₂

⇒P₂ = P/8

but we know at normal Temperature and pressure, pressure P = 1 atm

so, P₂ = 1/8 = 0.125 atm

therefore final pressure of gas is 0.125 atm