Question:
Calculate the work done if 1 mole of gas compressed isothermally and reversibly at 300 K from initial pressure 1 bar to final pressure 2 bar [$R=8.314~J~K^{-1}mol^{-1}$]
Calculate the work done if 1 mole of gas compressed isothermally and reversibly at 300 K from initial pressure 1 bar to final pressure 2 bar [$R=8.314~J~K^{-1}mol^{-1}$]
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Compression work is positive; expansion work is negative.
Updated On: Jun 19, 2026
- 1.729 kJ
- 0.865 kJ
- 2.593 kJ
- 3.458 kJ
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The Correct Option is A
Solution and Explanation
Step 1: Formula
$W = 2.303~nRT \log(P_{2}/P_{1})$
Step 2: Analysis
- $n = 1, R = 8.314, T = 300, P_{2} = 2, P_{1} = 1$. - $W = 2.303 \times 1 \times 8.314 \times 300 \times \log(2/1)$ - $W = 5744.1 \times 0.3010 \approx 1729~J$
Step 3: Conclusion
$1729~J = 1.729~kJ$. Final Answer: (A)
$W = 2.303~nRT \log(P_{2}/P_{1})$
Step 2: Analysis
- $n = 1, R = 8.314, T = 300, P_{2} = 2, P_{1} = 1$. - $W = 2.303 \times 1 \times 8.314 \times 300 \times \log(2/1)$ - $W = 5744.1 \times 0.3010 \approx 1729~J$
Step 3: Conclusion
$1729~J = 1.729~kJ$. Final Answer: (A)
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