A gaseous mixture enclosed in a vessel consists of one gram mole of a gas A with `gamma=(5/3)` and some amount of gas B with `gamma=7/5` at a temperature T.
The gases A and B do not react with each other and are assumed to be ideal. Find the number of gram moles of the gas B if `gamma` for the gaseous mixture is `(19/13)`.

Explanation

To solve the problem, we will use the concept of specific heat capacities and the definition of the heat capacity ratio (gamma) for the gaseous mixture.

### Step-by-Step Solution:

1. **Understanding the given information**:
- We have gas A with 1 gram mole, \( \gamma_A = \frac{5}{3} \).
- We have gas B with an unknown number of moles \( n_B \) and \( \gamma_B = \frac{7}{5} \).
- The total \( \gamma \) for the mixture is given as \( \frac{19}{13} \).
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