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 m^3, what is the final
volume of the gas?
a. 2 m^3
b. 1 m^3
c. 0.5 m^3
d. 0.25 m^3
e. 0.125 m^3
p1V1 =p2V2
V2=p1V1/p2
d. 0.25 m^3
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is held constant.
Boyle's Law 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 problem, we are given the initial pressure (P1 = 45 kPa) and initial volume (V1 = 0.5 m^3), the final pressure (P2 = 90 kPa), and we need to find the final volume (V2).
Plugging these values into the equation, we have:
45 kPa * 0.5 m^3 = 90 kPa * V2
Now we can solve for V2:
V2 = (45 kPa * 0.5 m^3) / 90 kPa
Simplifying the expression, we get:
V2 = 0.25 m^3
Therefore, the final volume of the gas is 0.25 m^3, which is option d. 0.25 m^3.