Question

At 273 K the maximum work done when pressure on 10 g of hydrogen is reduced from 10 atm to 1 atm under isothermal, reversible conditions is

• A. -52.18 kJ
• B. +26.09 kJ
• C. -26.09 kJ
• D. +52.18 kJ

Hint:

Work in isothermal process involves pressure ratio logarithm and number of moles.

Answer 1

The Correct Option is C

Step 1: Use formula for work in isothermal expansion/compression
\[ W = - nRT \ln \frac{P_2}{P_1} \] where \(n\) moles, \(R = 8.3\, J/mol \cdot K\), \(T = 273 K\), \(P_1 = 10 atm\), \(P_2 = 1 atm\).
Step 2: Calculate number of moles
Molar mass of H\(_2\) = 2 g/mol, \[ n = \frac{10}{2} = 5\, mol \] Step 3: Calculate work
\[ W = - 5 \times 8.3 \times 273 \times \ln \left(\frac{1}{10}\right) = -5 \times 8.3 \times 273 \times (-2.302) = -26,090\, J = -26.09\, kJ \] Step 4: Conclusion
Maximum work done is -26.09 kJ (work done by the system).