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One mole of an ideal gas expands at a constant temperature of 300 K from an initial volume of 10 litres to a final volume of 20 litres. The work done (in J) in expanding the gas is
(R = 8.31 J/mole-K) (log 2 = 0.3010)
    Correct answer is '1728'. Can you explain this answer?
    Verified Answer
    One mole of an ideal gas expands at a constant temperature of 300 K fr...
    Amount of work done in an isothermal expansion is given by

    = 1728.98J ≈ 1728 J
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    One mole of an ideal gas expands at a constant temperature of 300 K fr...
    Given:
    - Temperature (T) = 300 K
    - Initial volume (V1) = 10 L
    - Final volume (V2) = 20 L
    - Gas constant (R) = 8.31 J/mole-K
    - log 2 = 0.3010

    To find: Work done in expanding the gas (W)

    Formula:
    Work done by an ideal gas during expansion is given by the equation:
    W = -nRT ln(V2/V1)

    Where:
    - W is the work done
    - n is the number of moles of gas
    - R is the gas constant
    - T is the temperature in Kelvin
    - ln is the natural logarithm function
    - V2 is the final volume
    - V1 is the initial volume

    Calculation:
    - Given that the gas is ideal, we can assume that there is only one mole of gas present (n = 1).
    - Substituting the given values into the formula:
    W = - (1 mole) * (8.31 J/mole-K) * (300 K) * ln(20 L/10 L)

    Step 1: Calculate the ratio of final volume to initial volume:
    V2/V1 = 20 L / 10 L = 2

    Step 2: Calculate the natural logarithm of the ratio:
    ln(2) = 0.3010 (given)

    Step 3: Substitute the values into the formula and calculate the work done:
    W = - (1 mole) * (8.31 J/mole-K) * (300 K) * (0.3010)

    Step 4: Simplify the expression:
    W = - (1) * (8.31) * (300) * (0.3010) J

    W = - 747.459 J

    Step 5: The work done should be positive, so take the absolute value:
    W = 747.459 J

    Step 6: Round the answer to the nearest whole number:
    W ≈ 747 J

    The correct answer is 747 J.
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