Question

Calculate work done in isothermal reversible expansion of 1 mole ideal gas from initial pressure 10 bar to final pressure 1 bar at 300 K . \(\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\).

• A. -2.87 kJ
• B. -8.60 kJ
• C. -5.74 kJ
• D. -11.49 kJ

Hint:

For an isothermal reversible process use the pressure form of the work formula.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For an isothermal reversible expansion, \(W = -2.303\,nRT\log_{10}\dfrac{P_1}{P_2}\).

Step 2: Values
\(n = 1\), \(T = 300\) K, \(\dfrac{P_1}{P_2} = \dfrac{10}{1} = 10\), \(\log 10 = 1\).

Step 3: Calculation
\(W = -2.303\times 8.314\times 300\times 1\)
\(W \approx -5744\ \text{J} = -5.74\ \text{kJ}\)

Final Answer:
The work done is about \(-5.74\) kJ. \[ \boxed{\text{(C) }-5.74\text{ kJ}} \]