દ્વિપરમાણ્વિક વાયુ માટે, જો દ્રઢ અણુઓ માટે \(\gamma_1=\left(\frac{C p}{C v}\right)\) અને કંપન પ્રકારો પણ ધરાવતા અન્ય દ્વિપરમાણ્વિક અણુઓ માટે \(\gamma_2=\left(\frac{C p}{C v}\right)\) હોય, તો નીચેનામાંથી કયો વિકલ્પ સાચો છે? (Cp અને Cv એ વાયુની અચળ દબાણે અને અચળ કદે વિશિષ્ટ ઉષ્માઓ છે)

A \(\gamma_2=\gamma_1\)
B \(2 \gamma_2=\gamma_1\)
C \(\gamma_2 \lt \gamma_1\)
D \(\gamma_2\gt\gamma_1\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\gamma_2 \lt \gamma_1\)

Step-by-step Solution

Detailed explanation

દ્રઢ દ્વિપરમાણ્વિક અણુઓ માટે \(\begin{array}{ll} & f=5 \\ \therefore & \gamma_1=\frac{7}{5}=1.4 \end{array}\) કંપન પ્રકારો ધરાવતા દ્વિપરમાણ્વિક અણુઓ માટે \(\begin{array}{ll} & f=5+2=7 \\ & \gamma_2=\frac{9}{7}=1.28 \\ \therefore & \gamma_1>\gamma_2 \end{array}\)

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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