Question

For a gas \(\dfrac{R}{C_v} = 0.67\). This gas is made up of molecules which are

• A. diatomic
• B. polyatomic
• C. monoatomic
• D. mixture of diatomic and polyatomic

Hint:

Monoatomic gases have 3 translational degrees of freedom, giving \(C_v = \frac{3}{2}R\).

Answer 1

The Correct Option is C

Step 1: Relation between \(C_v\) and degrees of freedom.
For an ideal gas, \[ C_v = \frac{f}{2}R, \] where \(f\) is the number of degrees of freedom.
Step 2: Using the given ratio.
\[ \frac{R}{C_v} = \frac{2}{f}. \] Given \[ \frac{R}{C_v} = 0.67 \approx \frac{2}{3}. \]
Step 3: Determining degrees of freedom.
\[ \frac{2}{f} = \frac{2}{3} \Rightarrow f = 3. \]
Step 4: Identifying the gas.
A gas with 3 degrees of freedom is monoatomic.
Step 5: Conclusion.
The gas is monoatomic.