Question

For ideal non-rigid diatomic gas, the value of \(\frac{R}{C_V}\) is nearly \((\gamma = \frac{C_P}{C_V} = \frac{9}{7})\)

• A. \(0.4\)
• B. \(0.66\)
• C. \(0.28\)
• D. \(1.28\)

Hint:

Always use: \(\gamma = 1 + \frac{R}{C_V}\)

Answer 1

The Correct Option is C

Concept:
\[ \gamma = \frac{C_P}{C_V}, \quad C_P - C_V = R \] Step 1: Use relation. \[ \gamma = \frac{C_V + R}{C_V} = 1 + \frac{R}{C_V} \]
Step 2: Substitute value of \(\gamma\). \[ \frac{9}{7} = 1 + \frac{R}{C_V} \] \[ \frac{R}{C_V} = \frac{9}{7} - 1 = \frac{2}{7} \]
Step 3: Calculate. \[ \frac{2}{7} \approx 0.28 \]
Step 4: Conclusion. \[ \frac{R}{C_V} = 0.28 \]