Consider two diatomic ideal gases A &B at some temperature T. Molecules of A rigid and have mass 2m. Molecules of B have vibrational modes in addition and have mass m.The ratio of the specific heats `( C_(v) ^(4) ` & ` C_(v) ^(B))` of gas A &B,if both the molecules have planar structure is `:`

Options

A. (a)`( 5)/(7)`
B. (b)`( 5)/(6)`
C. (c)`( 6)/(7)`
D. (d)`(3)/( 4)`

Explanation

To solve the problem, we need to calculate the specific heats \( C_v \) for both diatomic gases A and B and then find the ratio of these specific heats.

### Step 1: Determine the degrees of freedom for gas A
Gas A is a diatomic ideal gas with rigid molecules. For a diatomic gas, the degrees of freedom \( F \) are given by:
\[ F = 3 + 2 = 5 \]
Here, 3 degrees of freedom correspond to translational motion (x, y, z) and 2 degrees of freedom correspond to rotational motion (rotation about two axes).
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