Equal volumes of two monoatomic gases,`A,B,`at the same temperature and pressure are mixed.The ratio of specific heats`(C_(p)//C_(v))`of the mixture will be
(a)1.50
(b)3.3
(c)1.67
(d)0.83

Options

A. `1.50`
B. `3.3`
C. `1.67`
D. `0.83`

Explanation

To solve the problem, we need to find the ratio of specific heats \( \frac{C_p}{C_v} \) for a mixture of two monoatomic gases \( A \) and \( B \) at the same temperature and pressure.

### Step-by-Step Solution:

1. **Identify the specific heats of monoatomic gases**:
- For a monoatomic gas, the specific heat at constant pressure \( C_p \) is given by:
\[ C_p = \frac{5}{2} R \]
- The specific heat at constant volume \( C_v \) is given by:
\[ C_v = \frac{3}{2} R \]

2. **Calculate the ratio \( \frac{C_p}{C_v} \)**:
- We can find the ratio of \( C_p \) to \( C_v \) using the values obtained:
\[ \frac{C_p}{C_v} = \frac{\frac{5}{2} R}{\frac{3}{2} R} \]

3. **Simplify the ratio**:
- The \( R \) in the numerator and denominator cancels out:
\[ \frac{C_p}{C_v} = \frac{5/2}{3/2} = \frac{5}{3} \]

4. **Convert the fraction to a decimal**:
- Now, we can convert \( \frac{5}{3} \) into a decimal:
\[ \frac{5}{3} \approx 1.67 \]

5. **Conclusion**:
- Therefore, the ratio of specific heats \( \frac{C_p}{C_v} \) for the mixture of the two monoatomic gases is:
\[ \frac{C_p}{C_v} = 1.67 \]

### Final Answer:
The correct option is (c) 1.67.