Two nonconducting containers having volume `V_(1)` and `V_(2)` contain monoatomic and dimatomic gases respectivley. They are connected as shown in figure. Pressure and temperature in the two containers are `P_(1), T_(1)` and `P_(2), T_(2)` respectively. Initially stop cock is closed, if the stop coc is opened find the final pressure and temperature.

Explanation

To solve the problem, we need to find the final pressure and temperature of the gases in two connected non-conducting containers after the stopcock is opened. The containers have volumes \( V_1 \) and \( V_2 \), and contain monoatomic and diatomic gases with initial pressures \( P_1 \), \( P_2 \) and temperatures \( T_1 \), \( T_2 \) respectively.

### Step-by-Step Solution:

1. **Calculate the Number of Moles**:
- For the monoatomic gas in container 1:
\[
n_1 = \frac{P_1 V_1}{R T_1}
...