An ideal gas at 27°C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is: (Given γ = 5/3)
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An ideal gas at 27°C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is: (Given γ = 5/3)

G1 Physics · Accepted Answer

Step 1: For an adiabatic ideal-gas process, TVᵞ⁻¹ = constant. Step 2: T₁ = 27 + 273 = 300 K, γ − 1 = 2/3 and V₁/V₂ = 27/8. Step 3: T₂/T₁ = (V₁/V₂)ᵞ⁻¹ = (27/8)²ᐟ³ = (3/2)² = 9/4. Step 4: T₂ = 300 × 9/4 = 675 K = 402°C. Step 5: Temperature rise = 675 − 300 = 375 K, numerically 375°C. Final answer: (D) 375°C.