JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases

Match the \(\frac{C _{ P }}{ C _{ v }}\) ratio for ideal gases with different type of molecules

Moleculae type \(\frac{C _{ P }}{ C _{ v }}\)

\((A)\) Monoatomic \((I)\) \(\frac{7}{ 5}\)

\((B)\) Diatomic rigid molecules \((II)\) \(\frac{9}{7}\)

\((C)\) Diatomic non-rigid molecules \((III)\) \(\frac{4}{3}\)

\((D)\) Triatomic rigid molecules \((IV)\) \(\frac{5}{3}\)

A \(A-IV, B-I, C-II, D-III\)
B \(A-IV, B-II, C-I, D-III\)
C \(A-III, B-IV, C-II, D-I\)
D \(A-II, B-III, C-I, D-IV\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(A-IV, B-I, C-II, D-III\)

Step-by-step Solution

Detailed explanation

\(\gamma=\frac{ C _{ p }}{ C _{ v }}=1+\frac{2}{ f }\) where \('f'\) is degree of freedom \((A)\) Monoatomic \(f=3, \gamma=1+\frac{2}{3}=\frac{5}{3}\) \((B)\) Diatomic rigid molecules, \(f=5, \gamma=1+\frac{2}{3}=\frac{7}{5}\) \((C)\) Diatomic non-rigid molecules…

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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Moleculae type	\(\frac{C _{ P }}{ C _{ v }}\)
\((A)\) Monoatomic	\((I)\) \(\frac{7}{ 5}\)
\((B)\) Diatomic rigid molecules	\((II)\) \(\frac{9}{7}\)
\((C)\) Diatomic non-rigid molecules	\((III)\) \(\frac{4}{3}\)
\((D)\) Triatomic rigid molecules	\((IV)\) \(\frac{5}{3}\)