What is the work done by an ideal gas during an isothermal expansion from volume

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Question: What is the work done by an ideal gas during an isothermal expansion from volume Vi to Vf?

Options:

Correct Answer: nRT ln(Vf/Vi)

Solution:

The work done by an ideal gas during an isothermal expansion is W = nRT ln(Vf/Vi).

What is the work done by an ideal gas during an isothermal expansion from volume Vi to Vf?

What is the work done by an ideal gas during an isothermal expansion from volume Vi to Vf?

Step 1: Understand that an isothermal expansion means the temperature of the gas remains constant.
Step 2: Know that 'n' represents the number of moles of the gas, 'R' is the ideal gas constant, and 'T' is the absolute temperature in Kelvin.
Step 3: Identify the initial volume (Vi) and the final volume (Vf) of the gas.
Step 4: Use the formula for work done during isothermal expansion, which is W = nRT ln(Vf/Vi).
Step 5: Calculate the natural logarithm of the ratio of the final volume to the initial volume, ln(Vf/Vi).
Step 6: Multiply the result from Step 5 by n, R, and T to find the total work done (W).

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