What is the work done when 1 mole of an ideal gas expands isothermally from 10 L

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Question: What is the work done when 1 mole of an ideal gas expands isothermally from 10 L to 20 L at 300 K? (R = 8.31 J/mol·K) (2023)

Options:

Correct Answer: 1660 J

Solution:

Work done = nRT ln(Vf/Vi) = 1 mol × 8.31 J/mol·K × 300 K × ln(20/10) = 1660 J.

What is the work done when 1 mole of an ideal gas expands isothermally from 10 L to 20 L at 300 K? (R = 8.31 J/mol·K) (2023)

What is the work done when 1 mole of an ideal gas expands isothermally from 10 L to 20 L at 300 K? (R = 8.31 J/mol·K) (2023)

Step 1: Identify the formula for work done during isothermal expansion of an ideal gas: Work done = nRT ln(Vf/Vi).
Step 2: Determine the values needed for the formula: n (number of moles) = 1 mol, R (ideal gas constant) = 8.31 J/mol·K, T (temperature) = 300 K, Vf (final volume) = 20 L, and Vi (initial volume) = 10 L.
Step 3: Calculate the ratio of final volume to initial volume: Vf/Vi = 20 L / 10 L = 2.
Step 4: Calculate the natural logarithm of the ratio: ln(2). You can use a calculator to find that ln(2) is approximately 0.693.
Step 5: Substitute all the values into the work done formula: Work done = 1 mol × 8.31 J/mol·K × 300 K × 0.693.
Step 6: Perform the multiplication: 1 × 8.31 × 300 × 0.693 = 1660 J.
Step 7: Conclude that the work done when the gas expands isothermally from 10 L to 20 L at 300 K is 1660 J.

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