Question

For a rigid diatomic molecule, universal gas constant \(R=nC_{p}\) where '\(C_{p}\)' is the molar specific heat at constant pressure. The value of fractional number '\(n\)' is

• A. \(4/9\)
• B. \(2/7\)
• C. \(3/8\)
• D. \(5/6\)

Hint:

A rigid diatomic molecule has 5 degrees of freedom, so \(C_{p}=\dfrac{7}{2}R\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
A rigid diatomic molecule has 5 degrees of freedom: 3 translational and 2 rotational.

Step 2: Calculation
\(C_{v}=\dfrac{5}{2}R\), so \(C_{p}=C_{v}+R=\dfrac{7}{2}R\).

Step 3: Express \(R\)
\(R=\dfrac{2}{7}C_{p}\), so \(n=\dfrac{2}{7}\).

Final Answer:
The value of n is 2/7. \[ \boxed{\text{(B) }\dfrac{2}{7}} \]