The pressure, P, of a gas varies inversely with its volume, V. Pressure is measured in units of Pa. Suppose that a particular amount of a gas is initially at a pressure of 84 Pa at a volume of 36 L. If the volume is expanded to 216 L, what will the new pressure be?
a) 6 Pa
b) 14 Pa
c) 216 Pa
d) 504 Pa <---- Right?
NO!! If the volume goes up the pressure goes down
P1 V1 = P2 V2
84 * 36 = P2 * 216
14 Pascals
To solve this problem, we need to use the relationship that the pressure of a gas varies inversely with its volume, which can be expressed mathematically as:
P ∝ 1/V
This means that if the volume (V) increases, the pressure (P) decreases, and vice versa.
We are given that the initial pressure (P1) is 84 Pa at a volume (V1) of 36 L. And we need to find the new pressure (P2) when the volume (V2) is expanded to 216 L.
To solve for P2, we can set up the following proportion:
P1 * V1 = P2 * V2
Substituting the given values, we have:
84 Pa * 36 L = P2 * 216 L
Simplifying further:
3024 = 216P2
Dividing both sides by 216:
3024 / 216 = P2
P2 ≈ 14
So, the new pressure (P2) will be approximately 14 Pa. Therefore, the correct option is (b) 14 Pa.
To solve this problem, we can use the inverse variation formula:
P ∝ 1/V
where P represents pressure and V represents volume.
From the given information, we have:
P1 = 84 Pa
V1 = 36 L
We're asked to find the new pressure, P2, when the volume is expanded to 216 L.
We can set up a proportion to solve for P2:
P1 * V1 = P2 * V2
Substituting the known values:
84 * 36 = P2 * 216
3024 = 216P2
Dividing both sides by 216:
P2 = 3024 / 216
P2 = 14
Therefore, the new pressure will be 14 Pa.
The correct answer is b) 14 Pa.