Understanding the Problem
To find the new pressure of oxygen gas when it is placed in a larger container while maintaining a constant temperature, we can use Boyle's Law. This law states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume.
Given Data
- Initial height of oxygen (h1) = 30 cm
- Initial pressure (P1) = Coating pressure (unknown)
- New container height (h2) = 200 cm
Using Boyle's Law
According to Boyle's Law:
P1 * V1 = P2 * V2
Where:
- V1 = Initial volume
- V2 = New volume
Since the height of the gas is proportional to its volume in a fixed cross-section container, we can relate the heights directly to the volumes:
- V1 = 30 cm
- V2 = 200 cm
Calculating the New Pressure
Now, let’s express the pressures in terms of the initial pressure:
- P1 * 30 cm = P2 * 200 cm
Rearranging the equation gives us:
P2 = (P1 * 30 cm) / 200 cm
Simplifying the Equation
- P2 = P1 * (30 / 200)
- P2 = P1 * (3 / 20)
This means that the new pressure (P2) is 3/20 of the initial pressure (P1).
Conclusion
By applying Boyle's Law, we find that the new pressure of the oxygen in the 200 cm container will be significantly reduced to 15% of the original coating pressure due to the increase in volume while keeping the temperature constant. Hence, as the volume increases, the pressure decreases proportionately.