For an enclosed gas at constant temperature, the relationship between pressure and volume is described by Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant.
Mathematically, this can be expressed as:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) and \( V_1 \) are the initial pressure and volume,
- \( P_2 \) and \( V_2 \) are the final pressure and volume.
Given that the pressure changes from 15 atm to 30 atm, we can set up the equation:
\[ 15 , \text{atm} \times V_1 = 30 , \text{atm} \times V_2 \]
To find the relationship between \( V_1 \) and \( V_2 \):
\[ V_2 = \frac{15 , \text{atm}}{30 , \text{atm}} V_1 \] \[ V_2 = \frac{1}{2} V_1 \]
This means that the volume of the gas becomes half of its original value.
Therefore, the correct response is:
The volume becomes half of its original value.