Calculate the specific heat capacity `C_(r)` of a gaseous mixture consisting of `v_(1)` moles of a gas of adiabatic exponent `gamma_(1)` and `v_(2)` moles of another gas of adiaqbatic exponent `gamma_(2)`.

Explanation

To calculate the specific heat capacity \( C_r \) of a gaseous mixture consisting of \( v_1 \) moles of a gas with adiabatic exponent \( \gamma_1 \) and \( v_2 \) moles of another gas with adiabatic exponent \( \gamma_2 \), we can follow these steps:

### Step-by-Step Solution

1. **Understand the relationship between specific heat capacities**:
The specific heat capacity at constant volume \( C_v \) and at constant pressure \( C_p \) are related by the equation:
\[
C_p - C_v = R
...