A gas at atmospheric pressure is compressed isothermally to one third of its volume. What is final pressure?
To determine the final pressure of a gas that is compressed isothermally, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law can be expressed mathematically as:
P1 * V1 = P2 * V2
Where:
P1 is the initial pressure
V1 is the initial volume
P2 is the final pressure
V2 is the final volume
In this case, the problem states that the gas is compressed to one third of its volume, so the final volume (V2) is one third of the initial volume (V1). Therefore, we have:
V2 = 1/3 * V1
Using this information, we can rewrite Boyle's Law as:
P1 * V1 = P2 * (1/3 * V1)
We can simplify this equation by canceling out V1:
P1 = P2 * (1/3)
To solve for the final pressure (P2), we rearrange the equation:
P2 = P1 / (1/3)
Since the initial pressure (P1) is given as atmospheric pressure, we can substitute its value and calculate the final pressure:
P2 = atmospheric pressure / (1/3)
Thus, the final pressure can be determined by dividing the atmospheric pressure by one-third.