Question

Calculate the constant external pressure required to expand 2 moles of an ideal gas from volume $15\text{dm}^3$ to $20\text{dm}^3$ if amount of work done is -600 J .

• A. 1.2 bar
• B. 1.5 bar
• C. 1.8 bar
• D. 2.1 bar

Hint:

Always convert Joules to $\text{bar dm}^3$ by dividing by 100 before solving for pressure or volume in these units.

Answer 1

The Correct Option is A

Step 1: Concept
The work done during the expansion of a gas against a constant external pressure is given by the formula $W = -P_{ext} \Delta V$.

Step 2: Meaning
Work is expressed in Joules ($J$), and pressure in bars. Note that $1 \text{ bar dm}^3 = 100 \text{ J}$. The change in volume $\Delta V$ is $V_2 - V_1$.

Step 3: Analysis
Given: $W = -600 \text{ J}$, $V_1 = 15 \text{ dm}^3$, $V_2 = 20 \text{ dm}^3$. $\Delta V = 20 - 15 = 5 \text{ dm}^3$. $W \text{ in bar dm}^3 = -600 / 100 = -6 \text{ bar dm}^3$. $-6 = -P_{ext} \times 5$. $P_{ext} = 6 / 5 = 1.2 \text{ bar}$.

Step 4: Conclusion
The constant external pressure required is $1.2 \text{ bar}$. Final Answer: (A)