The volume V of gas varies inversely as the pressure P on it. If the volume is 240 cm^3 under pressure of 30 kg/cm^2, what pressure has to be applied to have a volume of 160 cm^3 ?
V = k/P
So, PV is constant. You want P such that
P*160 = 30*240
45
How to answer math sudject
45 kg/cm²
Oh, pressure and volume... they really know how to play hide and seek! Let's see if we can find the answer by using a bit of mathematical clownery.
We know that the volume V is inversely proportional to the pressure P. This relationship can be represented mathematically as:
V = k/P
where k is a constant. Now, let's find the value of k using the given information.
When the volume V is 240 cm^3 and the pressure P is 30 kg/cm^2, we have:
240 = k/30
To solve for k, we can multiply both sides by 30:
k = 240 * 30
k = 7200
Now that we have the value of k, we can use it to find the pressure P when the volume is 160 cm^3:
160 = 7200/P
Solving for P, we can cross-multiply:
160P = 7200
Dividing both sides by 160, we find:
P = 7200/160
P = 45 kg/cm^2
Ta-da! The pressure that needs to be applied to have a volume of 160 cm^3 is 45 kg/cm^2. Just remember, pressure and volume are like a magic trick - they might change, but they always maintain their secret relationship!
To find the pressure that needs to be applied to have a volume of 160 cm³, we can use the formula for inverse variation. Inverse variation states that the product of the volume and the pressure remains constant.
Let's denote the initial volume as V₁ (240 cm³) and the initial pressure as P₁ (30 kg/cm²). We'll also denote the final volume as V₂ (160 cm³) and the unknown pressure as P₂.
Using the formula for inverse variation, we can write:
V₁ * P₁ = V₂ * P₂
Substituting the given values:
240 cm³ * 30 kg/cm² = 160 cm³ * P₂
Now, solve for P₂:
P₂ = (240 cm³ * 30 kg/cm²) / 160 cm³
Simplifying:
P₂ = (7200 kg*cm) / 160 cm³
P₂ = 45 kg/cm²
Therefore, a pressure of 45 kg/cm² needs to be applied to have a volume of 160 cm³.