Question

The work done in ergs for the reversible expansion of one mole of an ideal gas from a volume of 10 litres to 20 litres at 25°C is:

• A. \( 2.303 \times 298 \times 0.082 \log 2 \)
• B. \( 298 \times 10^7 \times 8.31 \times 2.303 \log 2 \)
• C. \( 2.303 \times 298 \times 0.082 \log 0.5 \)
• D. \( 8.31 \times 10^7 \times 298 \times -2.303 \log 0.5 \)

Hint:

For reversible processes involving an ideal gas, the work done is related to the logarithm of the ratio of final and initial volumes.

Answer 1

The Correct Option is A

For reversible expansion of an ideal gas, the work done is given by: \[ W = nRT \log \left( \frac{V_f}{V_i} \right) \] Substituting the values for \( n = 1 \), \( T = 298 \, \text{K} \), \( R = 0.082 \, \text{L·atm/mol·K} \), and \( V_f = 20 \, \text{L} \), \( V_i = 10 \, \text{L} \), the work done is: \[ W = 2.303 \times 298 \times 0.082 \log 2 \]
Final Answer: \[ \boxed{2.303 \times 298 \times 0.082 \log 2} \]