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: Understanding the Concept:
The work done ($W$) during the expansion or compression of a gas against a constant external pressure ($P_{\text{ext}}$) is given by the formula for irreversible thermodynamic work.
Step 2: Key Formula or Approach:
The formula for pressure-volume work is: \[ W = -P_{\text{ext}} \Delta V = -P_{\text{ext}} (V_2 - V_1) \] Step 3: Detailed Explanation:
Given data from the problem: Work done ($W$) = $-600 \text{ J}$ Initial volume ($V_1$) = $15\text{dm}^3 = 15 \text{ L}$ Final volume ($V_2$) = $20\text{dm}^3 = 20 \text{ L}$ Change in volume ($\Delta V$) = $V_2 - V_1 = 20 - 15 = 5\text{dm}^3 = 5 \text{ L}$ Substituting the known values into the work formula: \[ -600 \text{ J} = -P_{\text{ext}} \times 5 \text{ L} \] Solving for the external pressure $P_{\text{ext}}$: \[ P_{\text{ext}} = \frac{600 \text{ J}}{5 \text{ L}} = 120 \text{ J L}^{-1} \] To match the given options, we must convert the pressure units from $\text{J L}^{-1}$ to bar. We use the standard conversion factor: \[ 1 \text{ L bar} = 100 \text{ J} \implies 1 \text{ J L}^{-1} = \frac{1}{100} \text{ bar} \] Applying the conversion: \[ P_{\text{ext}} = 120 \times \left( \frac{1}{100} \text{ bar} \right) = 1.2 \text{ bar} \] Step 4: Final Answer:
The required constant external pressure is 1.2 bar.