The volume V of a gas varies inversely as the pressure P on it. If the volume is 250 cm3 under a pressure of 35 kg/cm3, solve for the pressure applied to have a volume of 180 cm3. Be sure to define your variables, find your constant variable, construct your variation equation, and then solve.
V = k/P, so
PV = k
you want P such that
180P = 250*35
By the way, pressure is in Pascals = N/m^2, not kg/cm^3
kg/cm^3 is density
To solve this problem, we can use the formula for inverse variation:
V = k/P
where V is the volume, P is the pressure, and k is the constant of variation.
First, let's define our variables:
V1 = 250 cm^3 (initial volume)
P1 = 35 kg/cm^3 (initial pressure)
V2 = 180 cm^3 (final volume)
P2 = ? (final pressure)
Next, let's find the constant of variation:
To find the constant of variation, we can substitute the initial values (V1 and P1) into the formula and solve for k:
V1 = k/P1
250 = k/35
To solve for k, we can cross multiply:
250 * 35 = k
8750 = k
So, the constant of variation is k = 8750.
Now, we can construct the variation equation:
V = 8750/P
Finally, let's solve for the final pressure:
We are given the final volume, V2 = 180 cm^3.
Substituting this into our variation equation, we get:
180 = 8750/P2
To solve for P2, we can cross multiply and solve for P2:
180 * P2 = 8750
P2 = 8750/180
Using a calculator, we can compute:
P2 ≈ 48.61 kg/cm^3 (rounded to two decimal places)
Therefore, the pressure applied to have a volume of 180 cm^3 is approximately 48.61 kg/cm^3.