Question

Two moles of an ideal gas at 1 bar pressure and 298 K is expanded into vacuum to double the volume. The work done is:

• A. \( 2 \, \text{J} \)
• B. \( 0 \, \text{J} \)
• C. \( 1.5 \, \text{J} \)
• D. \( 10 \, \text{J} \)

Hint:

In free expansion (expansion into vacuum), \( P_{\text{ext}}=0 \), so work done is always zero irrespective of volume change.

Answer 1

The Correct Option is B

Step 1: Identify the process.
The gas expands into vacuum, which is called free expansion.

Step 2: Write work formula.
\[ W = -\int P_{\text{ext}}\, dV \]

Step 3: Determine external pressure.
In vacuum, external pressure is zero:
\[ P_{\text{ext}} = 0 \]

Step 4: Substitute in work formula.
\[ W = -\int 0 \cdot dV \]
\[ W = 0 \]

Step 5: Physical interpretation.
Since there is no external resistance, the gas does no work during expansion.

Step 6: Important concept.
Work depends on external pressure, not internal pressure.

Step 7: Final conclusion.
\[ \boxed{0 \, \text{J}} \]