Question

An ideal gas expands from initial volume \(5 \text{dm}^3\) to \(15 \text{dm}^3\) against a constant external pressure of \(2\) atm. What is the work done by the gas ?

• A. \(-1202.6\) J
• B. \(-2026.4\) J
• C. \(-1101.32\) J
• D. \(-1013.2\) J

Hint:

For a constant external pressure, w = minus P times the change in volume; convert L atm to joules.

Answer 1

The Correct Option is B

Step 1: Plan:
Multiply pressure by the volume change in L atm, then convert the unit.

Step 2: Numbers:
Volume change is 10 dm$^3$, the same as 10 L. Then $2 \times 10 = 20$ L atm.
Convert: $20 \times 101.32 = 2026.4$ J.

Step 3: Sign:
The gas pushes outwards, so it does work on the surroundings and the work is negative: $-2026.4$ J, option (B).

Final Answer:
Option (B), $-2026.4$ J. \[ \boxed{\text{(B) } -2026.4\ \text{J}} \]