The ratio of specific heats `(C_p//C_v)` in case of gases of diatomie molecules is

Options

A. 1.4
B. 1.5
C. 1.6
D. 1.3

Explanation

To find the ratio of specific heats \( \frac{C_p}{C_v} \) for diatomic gases, we can follow these steps:

### Step 1: Understand the formula for the ratio of specific heats
The ratio of specific heats \( \frac{C_p}{C_v} \) can be expressed in terms of the degrees of freedom \( F \) of the gas molecules. The formula is given by:
\[ \frac{C_p}{C_v} = 1 + \frac{2}{F} \]

### Step 2: Determine the degrees of freedom for diatomic molecules
For diatomic gases, the degrees of freedom \( F \) is typically 5. This is because diatomic molecules can move in three-dimensional space (translational motion) and can also rotate about two axes (rotational motion). The vibrational modes are generally not considered at room temperature for basic calculations.

### Step 3: Substitute the degrees of freedom into the formula
Now that we know \( F = 5 \), we can substitute this value into the formula:
\[ \frac{C_p}{C_v} = 1 + \frac{2}{5} \]

### Step 4: Simplify the expression
To simplify \( 1 + \frac{2}{5} \):
\[ 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \]

### Step 5: Final result
Thus, the ratio of specific heats \( \frac{C_p}{C_v} \) for diatomic gases is:
\[ \frac{C_p}{C_v} = \frac{7}{5} \approx 1.4 \]

### Summary
The ratio of specific heats \( \frac{C_p}{C_v} \) for diatomic gases is \( \frac{7}{5} \) or approximately 1.4.

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