An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1 and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P2 , V2 and T2 , respectively. For this expansion,

Engineering

Chemistry

First Law and Various Process

Question

An ideal gas in a thermally insulated vessel at internal pressure = P₁, volume = V₁ and absolute temperature = T₁ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P₂ , V₂ and T₂ , respectively. For this expansion,

q = 0

P₂V₂ = P₁V₁

P₂V₂^γ = P₁V₁^γ

T₂ = T₁

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$∵$ P_ext = 0

$∴$ w = 0 $∵$ thermally insulated $∴$ q = 0

∴ ΔU = 0 , hence T₂ = T₁

$∴$ P₁V₁ = P₂V₂