MHT CET · Chemistry · Thermodynamics (C)
Equal masses in grams of \(\mathrm{H}_2, \mathrm{~N}_2, \mathrm{Cl}_2\), and \(\mathrm{O}_2\), are enclosed in cylinders separately. If these gases expand isothermally and reversibly by \(10 \mathrm{dm}^3\) at \(300 \mathrm{~K}\), the work done by gas is maximum for
- A \(\mathrm{H}_2\)
- B \(\mathrm{N}_2\)
- C \(\mathrm{Cl}_2\)
- D \(\mathrm{O}_2\)
Answer & Solution
Correct Answer
(A) \(\mathrm{H}_2\)
Step-by-step Solution
Detailed explanation
\(
\mathrm{W}_{\max }=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{V}_2}{\mathrm{~V}_1}
\)
Hence, \(\mathrm{W}_{\max } \infty \mathrm{n}\) (Given: R, T, \(\mathrm{V}_2, \mathrm{~V}_1=\) Constant)
\(\therefore \mathrm{W}_{\max } \propto \frac{1}{\mathrm{M} . \mathrm{W} .}\) (Given: equal mass)
Hence, lower the molecular mass, greater is the work done. Among the given, \(\mathrm{H}_2\) has the lowest molecular mass.
\mathrm{W}_{\max }=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{V}_2}{\mathrm{~V}_1}
\)
Hence, \(\mathrm{W}_{\max } \infty \mathrm{n}\) (Given: R, T, \(\mathrm{V}_2, \mathrm{~V}_1=\) Constant)
\(\therefore \mathrm{W}_{\max } \propto \frac{1}{\mathrm{M} . \mathrm{W} .}\) (Given: equal mass)
Hence, lower the molecular mass, greater is the work done. Among the given, \(\mathrm{H}_2\) has the lowest molecular mass.
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