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

Step 1: Understanding the Concept:
The ratio of the universal gas constant \(R\) to the molar specific heat at constant volume \(C_V\) can be expressed solely in terms of the adiabatic constant \(\gamma\).
Step 2: Key Formula or Approach:
Mayer's relation: \(C_P - C_V = R\)
Given: \(\gamma = C_P / C_V\)
Divide the Mayer's relation by \(C_V\): \[ \frac{C_P}{C_V} - \frac{C_V}{C_V} = \frac{R}{C_V} \implies \gamma - 1 = \frac{R}{C_V} \] Step 3: Detailed Explanation:
We are given \(\gamma = \frac{9}{7}\) for a non-rigid diatomic gas (where vibrational modes are also active).
Substitute the value of \(\gamma\) into the derived formula: \[ \frac{R}{C_V} = \frac{9}{7} - 1 \] \[ \frac{R}{C_V} = \frac{9 - 7}{7} = \frac{2}{7} \] Convert the fraction to a decimal: \[ \frac{2}{7} \approx 0.2857 \] Comparing this with the given options, \(0.28\) is the nearest value.
Step 4: Final Answer:
The value of \(R/C_V\) is approximately \(0.28\).