Question

Calculate the work done in joule if 1 mole of an ideal gas compressed from volume 24 dm$^3$ to 13 dm$^3$ at constant external pressure 3 bar.

• A. 3300 J
• B. 2250 J
• C. 4400 J
• D. 4870 J

Hint:

Sign convention is crucial!
- Expansion ($V_2 > V_1$): System does work, $W$ is negative.
- Compression ($V_2 < V_1$): Work is done on the system, $W$ is positive.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We must calculate the pressure-volume work ($W$) done during the irreversible compression of an ideal gas under a constant external pressure, and report the answer in Joules.

Step 2: Key Formula or Approach:
The formula for constant external pressure (irreversible) work is:
$$W = -P_{ext} \Delta V = -P_{ext} (V_2 - V_1)$$
To convert the work from standard pressure-volume units ($\text{bar } \text{dm}^3$ or $\text{bar } \text{L}$) into Joules, we must use the conversion factor:
$1 \text{ bar dm}^3 = 100 \text{ Joules}$.

Step 3: Detailed Explanation:
Given values:
External Pressure ($P_{ext}$) = $3 \text{ bar}$
Initial Volume ($V_1$) = $24 \text{ dm}^3$
Final Volume ($V_2$) = $13 \text{ dm}^3$
Substitute into the work formula:
$$W = -3 \times (13 - 24)$$
$$W = -3 \times (-11)$$
$$W = +33 \text{ bar dm}^3$$
The positive sign makes physical sense because work is being done on the system during compression.
Now, convert to Joules:
$$W = 33 \times 100 = 3300 \text{ J}$$

Step 4: Final Answer:
The work done is 3300 J, which corresponds to option (a).