A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27°C to 927°C. The pressure of the gas in the final state is:
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A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27°C to 927°C. The pressure of the gas in the final state is:

G1 Physics · Accepted Answer

Step 1: Temperatures in kelvin: T₁ = 27 + 273 = 300 K; T₂ = 927 + 273 = 1200 K. Step 2: Reversible adiabatic law for an ideal gas: TᵞP⁽¹⁻ᵞ⁾ = constant. Step 3: Therefore P₂/P₁ = (T₂/T₁)⁽ᵞ⁄⁽ᵞ⁻¹⁾⁾. Step 4: Compute the exponent γ/(γ − 1) = 1.4/0.4 = 3.5 = 7/2. Step 5: Temperature ratio T₂/T₁ = 1200/300 = 4. Step 6: P₂ = (2 atm) × 4⁽⁷⁄²⁾ = 2 × (2²)⁽⁷⁄²⁾ atm = 2 × 2⁷ atm = 256 atm. Final answer: (D) 256 atm.