A cylinder contains 0.1 cubic meters of gas at atmospheric pressure. This gas is allowed to expand until its pressure drops to 7800 Pa. What is the gas volume after this expansion has taken place?
answer: 7800/10130 = 0.770
To find the gas volume after the expansion, you can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Here's how you can calculate it:
1. Write down the given data:
- Initial gas volume: 0.1 cubic meters
- Initial pressure: atmospheric pressure (which we'll assume is 10130 Pa based on typical values)
- Final pressure: 7800 Pa
2. Apply Boyle's Law:
According to Boyle's Law, we have the equation:
P1 × V1 = P2 × V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
3. Substitute the given values into the equation:
10130 × 0.1 = 7800 × V2
4. Solve for V2:
V2 = (10130 × 0.1) / 7800
V2 = 1.013 cubic meters / 7800
V2 ≈ 0.0013 cubic meters
So, the gas volume after the expansion is approximately 0.0013 cubic meters.