Question:
Determine the constant external pressure required to compress \(2\) mole of an ideal gas from volume \(10.8\ \text{dm}^{3}\) to \(5.4\ \text{dm}^{3}\) if the work obtained is \(2460\) J.
Determine the constant external pressure required to compress \(2\) mole of an ideal gas from volume \(10.8\ \text{dm}^{3}\) to \(5.4\ \text{dm}^{3}\) if the work obtained is \(2460\) J.
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Work in compression against constant external pressure equals pressure times the decrease in volume.
Updated On: Nov 12, 2026
- \(2.28\) bar
- \(1.14\) bar
- \(3.42\) bar
- \(4.56\) bar
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
For compression at constant external pressure, the work done on the gas is \(w=P_{\text{ext}}\,(V_{1}-V_{2})\).
Step 2: Volume change
\(V_{1}-V_{2}=10.8-5.4=5.4\ \text{dm}^{3}=5.4\times10^{-3}\ \text{m}^{3}\), and \(w=2460\) J.
Step 3: Calculation
\(P_{\text{ext}}=\dfrac{2460}{5.4\times10^{-3}}=4.556\times10^{5}\ \text{Pa}\approx4.56\) bar, since \(1\ \text{bar}=10^{5}\) Pa.
Final Answer:
The external pressure required is about 4.56 bar. \[ \boxed{\text{(D) }4.56\ \text{bar}} \]
For compression at constant external pressure, the work done on the gas is \(w=P_{\text{ext}}\,(V_{1}-V_{2})\).
Step 2: Volume change
\(V_{1}-V_{2}=10.8-5.4=5.4\ \text{dm}^{3}=5.4\times10^{-3}\ \text{m}^{3}\), and \(w=2460\) J.
Step 3: Calculation
\(P_{\text{ext}}=\dfrac{2460}{5.4\times10^{-3}}=4.556\times10^{5}\ \text{Pa}\approx4.56\) bar, since \(1\ \text{bar}=10^{5}\) Pa.
Final Answer:
The external pressure required is about 4.56 bar. \[ \boxed{\text{(D) }4.56\ \text{bar}} \]
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