Step 1: Understand the scenarios for work done by gas.

When gas expands, work done (W) can be described in two scenarios:

• Constant Pressure Expansion: The work done by the gas when it expands at constant pressure can be calculated using the formula:
  W = P \Delta V = P(V_1 - V_0)
• Constant Temperature (Isothermal) Expansion: For an ideal gas expanding isothermally, the work done can be calculated using the equation:
  W = nRT \ln\left(\frac{V_1}{V_0}\right)

Step 2: Compare the work done in both cases.

Assuming the gas behaves ideally and the initial amount of gas is fixed:

• For constant pressure expansion (first case):
  W = P(V_1 - V_0)
• For constant temperature expansion (second case):
  W = nRT \ln\left(\frac{V_1}{V_0}\right)

Step 3: Determine conditions.

Under constant temperature (isothermal expansion), the temperature remains constant while volume increases, resulting in a greater change as the gas does work against external pressure.

We know that for an ideal gas, as the volume increases under isothermal conditions, the external work done can be relatively higher as opposed to the fixed pressure scenario.

Therefore, in an ideal scenario with significant expansion, the work done during constant temperature expansion usually exceeds that during constant pressure expansion due to the logarithmic nature of the expansion calculation.

Step 4: Conclusion.

Therefore, the gas does more work during the isothermal process than during the constant pressure process.

Thus, the answer is: Constant Temperature Expansion (Second Case does more work).