Adiabatic Compression of Ideal Gas

Steps:

• Insulated container implies adiabatic process: no heat exchange, follows PV^γ = constant (γ ≈ 1.4 for air).
• Adding 1 kg increases pressure by ΔP = mg/A; volume drops from 100 cm³ to 90 cm³, confirming compression raises P and T.
• For further compression, steeper PV^γ curve means same ΔP causes smaller ΔV than initial linear expectation.
• Additional 10 kg (total 11 kg) from 90 cm³ state yields ΔV < 10 cm³ due to higher starting P and T.

Why A is correct:

• Adiabatic law PV^γ = constant (γ > 1) makes P-V curve steeper than isothermal; larger ΔP from 90 cm³ causes proportionally smaller volume reduction.

Why the others are wrong:

• B: 9 kg cannot reduce volume to zero; gas pressure rises indefinitely per adiabatic relation, preventing collapse.
• C: Added mass increases total pressure above 1 atm, so trapped air pressure exceeds 1 atm at 90 cm³.
• D: Adiabatic compression increases temperature (work done on gas raises internal energy).

Final answer: A