To solve the problem of calculating the work done by a gas during expansion at constant pressure, we can use the formula for work done in a thermodynamic process: ### Formula for Work Done The work done \( W \) by a gas during expansion at constant pressure is given by the formula: \[ W = P \Delta V \] where: - \( W \) is the work done (in joules, J), - \( P \) is the constant pressure (in pascals, Pa), - \( \Delta V \) is the change in volume (in cubic meters, m³). ### Step-by-Step Solution 1. **Identify the Initial Volume**: The initial volume \( V_i \) of the gas is given as: \[ V_i = 2 \times 10^{-6} \, m^3 \] 2. **Calculate the Final Volume**: The gas expands to six times its initial volume. Therefore, the final volume \( V_f \) is: \[ V_f = 6 \times V_i = 6 \times (2 \times 10^{-6}) = 12 \times 10^{-6} \, m^3 \] 3. **Calculate the Change in Volume**: The change in volume \( \Delta V \) is calculated as: \[ \Delta V = V_f - V_i = (12 \times 10^{-6}) - (2 \times 10^{-6}) = 10 \times 10^{-6} \, m^3 \] 4. **Identify the Constant Pressure**: The constant pressure \( P \) is given as: \[ P = 2 \times 10^5 \, N/m^2 \] 5. **Calculate the Work Done**: Now, substituting the values of \( P \) and \( \Delta V \) into the work done formula: \[ W = P \Delta V = (2 \times 10^5) \times (10 \times 10^{-6}) \] \[ W = 2 \times 10^5 \times 10 \times 10^{-6} = 2 \times 10^5 \times 10^{-5} = 2 \times 10^0 = 2 \, J \] ### Conclusion The work done by the gas during its expansion at constant pressure is: \[ \boxed{2.0 \, J} \] ### Explanation of Other Options - **Option B (4.0 J)**: This option is incorrect because it likely results from a miscalculation of either the change in volume or the multiplication with pressure. - **Option C (12.0 J)**: This option is incorrect as it may stem from misunderstanding the relationship between pressure and volume change, possibly assuming a different process or misapplying the formula. - **Option D (2.4 J)**: This option is also incorrect, possibly due to an error in calculating the change in volume or misapplying the pressure value. ### Common Pitfalls - **Misunderstanding the Process**: Remember that the work done formula applies specifically to processes at constant pressure. - **Volume Units**: Ensure that all volume measurements are in cubic meters when using SI units. - **Pressure Units**: Always check that pressure is in pascals (N/m²) for consistency in calculations. ### Revision Summary - Work done by a gas at constant pressure is calculated using \( W = P \Delta V \). - Ensure to calculate the change in volume correctly by subtracting initial volume from final volume. - Always use consistent units (SI units) for pressure and volume. - Double-check calculations to avoid common errors in thermodynamic problems.