A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. What is the work done by the gas?

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Q: A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. What is the work done by the gas?

Solution: The work done in an isothermal expansion is W = nRT ln(Vf/Vi). Assuming 1 mole of gas, W = 1 * 8.31 * 300 * ln(2) ≈ 600 J.

Steps: 9

Step 1: Identify the initial volume (Vi) and final volume (Vf) of the gas. Here, Vi = 1 m³ and Vf = 2 m³.
Step 2: Identify the temperature (T) of the gas. Here, T = 300 K.
Step 3: Use the ideal gas constant (R). The value of R is approximately 8.31 J/(mol·K).
Step 4: Assume the number of moles of gas (n). In this case, we assume n = 1 mole.
Step 5: Use the formula for work done (W) during isothermal expansion: W = nRT ln(Vf/Vi).
Step 6: Substitute the values into the formula: W = 1 * 8.31 * 300 * ln(2).
Step 7: Calculate ln(2), which is approximately 0.693.
Step 8: Multiply the values: W = 1 * 8.31 * 300 * 0.693.
Step 9: Calculate the final result: W ≈ 600 J.