MHT CET · Chemistry · Thermodynamics (C)

Two moles of an ideal gas expand freely and isothermally from \(5 \mathrm{dm}^3\) to \(50 \mathrm{dm}^3\). What is the value of \(\Delta \mathrm{H}\) ?

A Zero kJ
B \(20 \mathrm{~kJ}\)
C \(100 \mathrm{~kJ}\)
D \(150 \mathrm{~kJ}\)

Verified Solution

Answer & Solution

Correct Answer

(A) Zero kJ

Step-by-step Solution

Detailed explanation

A free expansion means expansion against zero opposing force. \(\mathrm{P}_{\mathrm{ext}}=0\) and hence, \(\mathrm{W}=0\)
For isothermal process, \(\Delta \mathrm{U}=0\).
\(\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{P} \Delta \mathrm{V}=\Delta \mathrm{U}-\mathrm{W}\)
\(\Delta \mathrm{H}=0-0=0 \mathrm{~kJ}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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