The volume of a certain mass of gas at a pressure of `5 xx 10 ^(4) Pa ` is doubled adiabatically. What is the final pressure of the gas ? `[ gamma = 1.4]`

Explanation

To solve the problem of finding the final pressure of a gas after its volume is doubled adiabatically, we can use the adiabatic condition for an ideal gas, which states that \( PV^\gamma = \text{constant} \), where \( \gamma \) is the heat capacity ratio (given as 1.4).

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Initial Pressure, \( P_1 = 5 \times 10^4 \, \text{Pa} \)
- Initial Volume, \( V_1 \) (unknown, but we will express everything in terms of it)
- Final Volume, \( V_2 = 2V_1 \) (since the volume is doubled)
...