Under a pressure of 200 kPa, a confined gas has a volume of 2,500 cubic meters. The pressure acting on the gas is increased to 500 kPa. What is the new volume of the gas if the temperature remains the same?
P1 * V1 = P2 * V2
To determine the new volume of the gas, we can use Boyle's Law, which states that the product of the initial pressure (P1) and initial volume (V1) is equal to the product of the final pressure (P2) and final volume (V2), as long as the temperature remains constant.
Boyle's Law equation: P1 * V1 = P2 * V2
Given:
Initial pressure (P1) = 200 kPa
Initial volume (V1) = 2500 cubic meters
Final pressure (P2) = 500 kPa
Temperature remains constant
Let's plug in the values:
200 kPa * 2500 cubic meters = 500 kPa * V2
Now, we can solve for V2:
500,000 = 500 kPa * V2
To isolate V2, divide both sides of the equation by 500 kPa:
500,000 / 500 kPa = V2
V2 = 1000 cubic meters
Therefore, the new volume of the gas when the pressure is increased to 500 kPa while the temperature remains constant is 1000 cubic meters.
To find the new volume of the gas, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.
Boyle's Law equation: P1V1 = P2V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = New pressure
V2 = New volume
From the given information:
P1 = 200 kPa
V1 = 2,500 cubic meters
P2 = 500 kPa
We can rearrange the equation to solve for V2:
V2 = (P1 * V1) / P2
Plugging in the values we have:
V2 = (200 kPa * 2,500 cubic meters) / 500 kPa
Calculating this equation, we get:
V2 = 1,000 cubic meters.
Therefore, the new volume of the gas, when the pressure is increased to 500 kPa while the temperature remains the same, is 1,000 cubic meters.