Import Question JSON

$\text{Hint: Use work done formula}$ $\text{Step 1: Identify the type of process and the appropriate formula}$ $\text{The problem describes an isothermal expansion against a constant external pressure. Since the pressure is constant, we can use the formula:}$ $W = -P_{\text{ext}}\Delta V$ $\text{Where:}$ $P_{\text{ext}} = \text{external pressure} = 10^5 \text{ N/m}^2$ $\Delta V = V_f - V_i = \text{change in volume}$ $\text{Step 2: Calculate the change in volume}$ $V_i = 10^{-3} \text{ m}^3 \text{ (initial volume)}$ $V_f = 10^{-2} \text{ m}^3 \text{ (final volume)}$ $\Delta V = V_f - V_i = 10^{-2} - 10^{-3} = 9 \times 10^{-3} \text{ m}^3 = 0.009 \text{ m}^3$ $\text{Step 3: Calculate the work done by the gas}$ $W = -P_{\text{ext}}\Delta V$ $W = -10^5 \times [10^{-2} - 10^{-3}]$ $W = -10^5 \times 0.009$ $W = -900 \text{ J}$ $\text{The negative sign indicates that the gas is doing work on the surroundings during expansion.}$ $\text{Step 4: Verify the units and magnitude}$ $\text{The units are correct: N/m}^2 \times \text{m}^3 = \text{N} \cdot \text{m} = \text{J (joules)}$ $\text{The work done by the gas is -900 J, which corresponds to option 2.}$ $\text{Note: It's important to recognize that in thermodynamics, work done by a system (in this case, the gas) on the surroundings is conventionally given a negative sign. The gas is expanding and pushing against the external pressure, so it is doing work on the surroundings.}$