A) \[7.5\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]
B) \[7.0\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]
C) \[8.5J{{K}^{-1}}mo{{l}^{-1}}\]
D) \[8.0\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]
Correct Answer: D
Solution :
[d] Molar mass of the gas = 4g/mol Speed of sound \[V=\sqrt{\frac{\gamma RT}{m}}\Rightarrow 952=\sqrt{\frac{\gamma \times 3.3\times 273}{4\times {{10}^{-3}}}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\gamma =1.6=\frac{16}{10}=\frac{8}{5}\] Also, \[\gamma =\frac{{{C}_{P}}}{{{C}_{v}}}=\frac{8}{5}\] \[\text{So, }{{C}_{p}}=\frac{8\times 5}{5}=8J{{K}^{-1}}mo{{l}^{-1}}\] \[\left[ {{C}_{v}}=\text{ }5.0\text{ }J{{K}^{-1}}given \right]\]
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