Question

If 5 L of an ideal gas at a constant external pressure of 2 atm expands isothermally to a final volume of \( X \) L, the system does a work of -2,026.4 J. \( X \) (in L) is

• A. 25
• B. 20
• C. 15
• D. 10

Hint:

For isothermal expansion, remember that the work done depends on the change in volume and the external pressure.

Answer 1

The Correct Option is C

The work done during an isothermal expansion is given by the equation: \[ W = -P_{\text{ext}} \Delta V \] Where \( P_{\text{ext}} = 2 \, \text{atm} = 2 \times 101.32 \, \text{J} \, \text{L}^{-1} \), and \( \Delta V = X - 5 \, \text{L} \).
The work done is \( -2,026.4 \, \text{J} \), so we have the equation: \[ -2,026.4 = -2 \times 101.32 \times (X - 5) \] Solving for \( X \), we get \( X = 15 \, \text{L} \).