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Step-by-Step Solution
Step 1: Identify the Relevant Formula
In an isothermal expansion against a constant external pressure, the work done (W) by a gas can be calculated using the expression:
$$W = - P_{ext} \,\bigl(V_{2} - V_{1}\bigr)$$
The negative sign indicates that the system (gas) is doing work on the surroundings.
Step 2: Note the Given Values
External pressure, $$P_{ext} = 2 \text{ bar}$$
Initial volume, $$V_{1} = 0.1 \text{ L}$$
Final volume, $$V_{2} = 0.25 \text{ L}$$
Conversion factor: $$1 \text{ L bar} = 100 \text{ J}$$
Step 3: Substitute the Values into the Formula
Calculate the change in volume:
$$\Delta V = V_{2} - V_{1} = 0.25 \text{ L} - 0.1 \text{ L} = 0.15 \text{ L}$$
Then, apply it to the work expression:
$$W = - (2 \text{ bar}) \times (0.15 \text{ L})$$
Step 4: Calculate the Work in L·bar
Multiplying,
$$W = - (2 \times 0.15) \text{ bar·L} = -0.30 \text{ bar·L}$$
Step 5: Convert Bar·L to Joules
Using the conversion factor,
$$W = -0.30 \, (\text{bar·L}) \times 100 \frac{\text{J}}{\text{bar·L}} = -30 \text{ J}$$
Step 6: State the Final Answer
Hence, the work done by the gas is
$$\boxed{-30 \text{ J}}.$$
