B

Step 1: Understand the process
We have a piston-cylinder arrangement where the product of pressure (P) and volume (V) remains constant during the process. This is known as an isothermal process for an ideal gas.

Step 2: Identify the initial state
Initial pressure, P₁ = 200 kPa = 200,000 Pa
Initial volume, V₁ = 2 m³

Step 3: Identify the final state
Final pressure, P₂ = 100 kPa = 100,000 Pa. Since PV is constant, we can find the final volume, V₂.
Using the relation:
P₁ V₁ = P₂ V₂
200 kPa * 2 m³ = 100 kPa * V₂
400,000 = 100,000 * V₂
V₂ = \frac{400,000}{100,000} = 4 m³

Step 4: Calculate the work done
The work done by the gas during expansion can be calculated using the formula for work done during a process with constant PV:
W = P * (V₂ - V₁)
W = 100,000 Pa * (4 m³ - 2 m³)
W = 100,000 Pa * 2 m³ = 200,000 J or 200 kJ

Final Answer: The work done by the gas on the piston is 200 kJ.