According to Boyle's Law, if the volume is 50 gallons at 20 atm, what is the volume at 40 atm?

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. This relationship can be expressed with the formula:

P1 × V1 = P2 × V2

Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

In the given question, you start with a volume (V1) of 50 gallons at an initial pressure (P1) of 20 atm. You are asked to find the new volume (V2) when the pressure is increased to 40 atm (P2).

Using Boyle's Law:

20 atm × 50 gallons = 40 atm × V2

To solve for V2, rearranging the equation gives:

V2 = (20 atm × 50 gallons) / 40 atm

Calculating this yields:

V2 = 1000 / 40 = 25 gallons

Thus, at a pressure of 40 atm, the new volume of the gas would be 25 gallons. This confirms that under increased pressure, the volume decreases, illustrating Boyle's Law effectively.