For an enclosed gas with a constant temperature, the pressure of the gas changes from 15 atm to 30 atm. What happens to the volume of the gas?(1 point)

Responses

The volume stays the same as its original value.
The volume stays the same as its original value.

The volume becomes two times the original value.
The volume becomes two times the original value.

The volume becomes half of its original value.
The volume becomes half of its original value.

The volume becomes 15 times the original value.

1 answer

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.