Question

One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litres. Then \( \Delta S \) (cal deg\(^{-1}\) mol\(^{-1}\)) for this process is: \( R = 2 \, \text{cal K}^{-1} \text{mol}^{-1} \)

• A. 7.12
• B. 8.314
• C. 4.6
• D. 3.95

Hint:

For isothermal expansion, the entropy change depends on the ratio of final to initial volume.

Answer 1

The Correct Option is C

Step 1: Entropy Change for Isothermal Expansion.
The entropy change for an ideal gas during an isothermal expansion is given by: \[ \Delta S = nR \ln \left(\frac{V_f}{V_i}\right) \] Substitute the given values to calculate \( \Delta S \). The result is 4.6 cal K\(^{-1}\) mol\(^{-1}\).
Step 2: Conclusion.
The correct answer is (C), 4.6.