At 27°C, a gas is compressed suddenly such that its pressure becomes (1/8) of original pressure. Final temperature will be (γ = 5/3):
Options

Question

At 27°C, a gas is compressed suddenly such that its pressure becomes (1/8) of original pressure. Final temperature will be (γ = 5/3):

G1 Physics · Accepted Answer

Step 1: For an adiabatic ideal-gas process, TᵞP¹⁻ᵞ = constant, equivalently T₂/T₁ = (P₂/P₁)⁽ᵞ⁻¹⁾ᐟᵞ. Step 2: T₁ = 27 + 273 = 300 K, γ = 5/3, so (γ − 1)/γ = (2/3)/(5/3) = 2/5. Step 3: P₂/P₁ = 1/8. Thus T₂ = 300 × (1/8)²ᐟ⁵ ≈ 130.6 K. Step 4: Convert to Celsius: T₂ ≈ 130.6 − 273 = −142.4°C. Final printed answer: (C) −142°C. Important: A reduction of pressure by a factor of 8 is consistent with an adiabatic expansion rather than “compression” as written in the source.