Question

A work is done on the system such that one mole of an ideal gas at 400K is compressed isothermally and reversibly to 1/10th of its original volume. The amount of (use R=2 cal) work done will be

• A. 2.303 k-cal
• B. 0.184 k-cal
• C. 1.84 k-cal
• D. 4.60 k-cal

Hint:

For isothermal processes, the work done can be determined by the equation involving the logarithmic ratio of the final and initial volumes.

Answer 1

The Correct Option is C

For an isothermal and reversible compression, the work done on the system can be calculated using the formula: \[ W = -nRT \ln\left(\frac{V_f}{V_i}\right) \] Here, \(n = 1\) mole, \(R = 2\) cal/mol·K, \(T = 400\) K, and the volume ratio \(V_f/V_i = 1/10\).
Substituting these values: \[ W = -1 \times 2 \times 400 \times \ln\left(\frac{1}{10}\right) = 1.84 \, \text{kcal} \]