The volume V of a gas varies inversely as pressure P is exerted. If V = 4 liters when P = 3.5 atmospheres, find V when P = 2.5 atmospheres. Note: Round your answer to the nearest thousandth.
To solve this problem, we need to use the concept of inverse variation. Inverse variation is represented mathematically as:
V ∝ 1/P
Where V is the volume of the gas and P is the pressure exerted.
We can rewrite this equation as:
V = k/P
Where k is a constant of variation.
To find the value of k, we can use the given information. We know that when V = 4 liters, P = 3.5 atmospheres. Plugging these values into the equation, we get:
4 = k/3.5
To find the value of k, we can multiply both sides of the equation by 3.5:
4 * 3.5 = k
k = 14
Now that we have the value of k, we can use it to find V when P = 2.5 atmospheres. Plugging the values into the equation, we get:
V = 14/2.5
V ≈ 5.6
Therefore, when P = 2.5 atmospheres, the volume of the gas is approximately 5.6 liters.
"The volume V of a gas varies inversely as pressure P is exerted" -->
v = k(1/p) , where k is a constant
given:
when v=4, p=3.5
4= k/3.5
k = 4(3.5) = 14
v = 14/p
plug in p = 2.5 to find v