Work by gas equals external pressure times volume change

Steps:

• Identify work done by gas during expansion as force by external pressure times displacement.
• External pressure is atmospheric, constant for this setup.
• Volume change ΔV = cross-sectional area A times piston displacement r.
• Thus, work W = (atmospheric pressure) × A × r.

Why A is correct:

• Matches thermodynamic formula for irreversible expansion work: W = P_ext ΔV, where P_ext is atmospheric pressure and ΔV = A r.

Why the others are wrong:

• B: Uses internal gas pressure, but work is against external pressure, not internal.
• C: Uses internal pressure and s (final gas column length), but displacement is r, not s.
• D: Uses correct pressure but wrong distance s instead of displacement r.

Final answer: A