Question

Calculate the work done when \(1\) mole of an ideal gas is expanded reversibly and isothermally from initial pressure \(10\) bar to final pressure \(1\) bar at constant temperature \(300\) K. [\(R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}\)]

• A. \(-5.744\) kJ
• B. \(-5.123\) kJ
• C. \(-6.514\) kJ
• D. \(-4.981\) kJ

Hint:

Use $w=-2.303\,nRT\log\frac{P_1}{P_2}$ for reversible isothermal expansion.

Answer 1

The Correct Option is A

Step 1: Use the natural log
$w=-nRT\ln\frac{P_1}{P_2}=-1\times8.314\times300\times\ln10$.
$\ln10=2.303$, so
\[ w=-2494.2\times2.303=-5744\text{ J} \]

Step 2: Result
$w=-5.744$ kJ, option (A). The other values come from wrong constants or temperatures.

Final Answer:
$-5.744$ kJ, option (A). \[ \boxed{\text{(A)}} \]