Q. 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
A) 256 atm
B) 8 atm
C) 28 atm
D) 68.7 atm
Explanation
[Solution from source] For an adiabatic process P^(1−γ)T^γ is constant, so P ∝ T^(γ/(γ−1)) = T^3.5. T rises from 300 K to 1200 K, a factor of 4, so P₂ = 2 × 4^3.5 = 2 × 128 = 256 atm. Using Celsius temperatures or P ∝ T (isochoric) gives the wrong values. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.