Question

For a gas, \(\frac{R}{C_v} = 0.4\) where R is the universal gas constant and \(C_v\) is the molar specific heat at constant volume. The gas is made up of molecules which are

• A. monoatomic
• B. polyatomic
• C. non rigid diatomic
• D. rigid diatomic

Hint:

R/Cv = 0.4 gives Cv = 5R/2, which is a rigid diatomic gas.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The molar specific heat at constant volume is \(C_v=\dfrac f2R\), where \(f\) is the number of degrees of freedom.

Step 2: Use the given ratio:
\(\dfrac{R}{C_v}=0.4\), so \(C_v=\dfrac{R}{0.4}=2.5R=\dfrac52R\). That means \(f=5\).

Step 3: Match to the gas type:
A monatomic gas has \(f=3\). A rigid diatomic gas has \(f=5\) (3 translational + 2 rotational). A non-rigid diatomic gas has \(f=7\). So the gas is rigid diatomic. Option D.

Step 4: Why the other options are wrong.
Monatomic gas gives \(C_v=1.5R\), so \(R/C_v=0.67\). Non-rigid diatomic gives \(C_v=3.5R\), so \(R/C_v=0.286\).

Final Answer:
The gas is made of rigid diatomic molecules. \[ \boxed{\text{(D) }\text{rigid diatomic}} \]