If for a gas, $\frac{R}{C_{P}}=0.285$, this gas is made up of molecules which are

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Professor PC Thomas Classes · Answer

(a) : Given $\frac{R}{C_P} = 0.285 \approx \frac{2}{7}$. Since $R = C_P - C_V$, we have $\frac{C_P - C_V}{C_P} = \frac{2}{7}$. This gives $1 - \frac{C_V}{C_P} = \frac{2}{7}$, so $1 - \frac{1}{\gamma} = \frac{2}{7}$, meaning $\frac{1}{\gamma} = \frac{5}{7}$. Therefore, $\gamma = 1.4$. A specific heat ratio of $1.4$ corresponds to a diatomic gas.