The only incorrect statement for the value of $γ$ for ${NH}_{3}$ gas is: (Assume ideal gas behaviour).

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$γ = \frac{10}{9}$ at very high temperature

$γ = \frac{5}{3}$ at very low temperature

$γ = \frac{7}{5}$ at moderate temperature

$γ = \frac{7}{6}$ considering only 50 % contribution of vibrational energy

answer is A.

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Detailed Solution

if only 50% contribution of vibration energy

$\begin{array}{l} f = 6 + (\frac{6}{2}) = 9 \\ C_{y} = \frac{9}{2} R \\ C_{p} = \frac{11}{2} R \Rightarrow y = \frac{11}{9} \end{array}$

At moderate temperature degree of freedom = f= 6

$\begin{array}{l} C_{v} = \frac{f}{2} R = 3 R C_{p} = 4 R \\ γ = \frac{C_{p}}{C_{v}} = \frac{4}{3} \end{array}$

$y = \frac{7}{6}$ for high temperature.

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