Question:
Calculate work done if 1 mole of an ideal gas expands isothermally from 2 dm$^3$ to 2.8 dm$^3$ against constant external pressure 1 atm.
Calculate work done if 1 mole of an ideal gas expands isothermally from 2 dm$^3$ to 2.8 dm$^3$ against constant external pressure 1 atm.
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Work done in irreversible expansion is $W = -P_{ext}\Delta V$. Use 101.325 J as the conversion factor for atm dm$^3$ to Joules.
Updated On: Apr 30, 2026
- -40.52 J
- -81.04 J
- -121.56 J
- -60.78 J
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The Correct Option is B
Solution and Explanation
Step 1: Formula
For expansion against constant external pressure: $W = -P_{ext} \Delta V$.
Step 2: Substitution
$P_{ext} = 1$ atm, $\Delta V = V_2 - V_1 = 2.8 - 2.0 = 0.8$ dm$^3$.
$W = -(1 \text{ atm}) \times (0.8 \text{ dm}^3) = -0.8$ atm dm$^3$.
Step 3: Conversion to Joules
$1 \text{ atm dm}^3 = 101.3$ J.
$W = -0.8 \times 101.3 = -81.04$ J.
Step 4: Conclusion
The work done is -81.04 J.
Final Answer:(B)
For expansion against constant external pressure: $W = -P_{ext} \Delta V$.
Step 2: Substitution
$P_{ext} = 1$ atm, $\Delta V = V_2 - V_1 = 2.8 - 2.0 = 0.8$ dm$^3$.
$W = -(1 \text{ atm}) \times (0.8 \text{ dm}^3) = -0.8$ atm dm$^3$.
Step 3: Conversion to Joules
$1 \text{ atm dm}^3 = 101.3$ J.
$W = -0.8 \times 101.3 = -81.04$ J.
Step 4: Conclusion
The work done is -81.04 J.
Final Answer:(B)
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