The pressure of a gas in a cylinder with a movable piston is increased from 45 kPa to 90 kPa. If the
temperature is held constant, and the initial volume of the gas in the cylinder is 0.5 m3, what is the final
volume of the gas?
a. 2 m3
b. 1 m3
c. 0.5 m3
d. 0.25 m3
To solve this problem, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its volume. Mathematically, this relationship can be expressed as:
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 this case, the initial pressure P1 is 45 kPa, the final pressure P2 is 90 kPa, and the initial volume V1 is 0.5 m3. We need to find the final volume V2.
Using the ideal gas law equation:
45 kPa * 0.5 m3 = 90 kPa * V2
Simplifying the equation:
22.5 = 90 * V2
Dividing both sides by 90:
22.5 / 90 = V2
V2 = 0.25 m3
Therefore, the final volume of the gas is 0.25 m3. The correct answer is option d. 0.25 m3.