The volume of a gas in cubic centimeters, V, varies inversely with the pressure of the gas in liters per square centimeter, p.

When the volume of the gas is 16 cm3, its pressure is 20 L/cm2. Find the volume of the gas when the pressure is 1.6 L/cm2.

the possible answers (for apex) are:

A. 512 cm^3
B. 20 cm^3
C. 200 cm^3
D. 819.2 cm^3

To find the volume of the gas when the pressure is 1.6 L/cm2, we can use the inverse variation formula:

V = k/p

where V is the volume, p is the pressure, and k is the constant of variation.

We are given the volume and pressure at another point:

V1 = 16 cm3
p1 = 20 L/cm2

Next, we find the value of the constant k using these values:

k = V1 * p1

k = 16 cm3 * 20 L/cm2

k = 320 cm3*L

Now we can use the formula with the new pressure (p2 = 1.6 L/cm2) to find the volume (V2):

V2 = k / p2

V2 = 320 cm3*L / 1.6 L/cm2

V2 = 200 cm3

Therefore, the volume of the gas when the pressure is 1.6 L/cm2 is 200 cm3.

To solve this problem, we can use the concept of inverse variation. Inverse variation states that when two variables are inversely proportional, their product remains constant.

Let's set up the equation using the given information:

V ∝ 1/p

Here, V represents the volume of the gas in cm^3, and p represents the pressure of the gas in L/cm^2.

We can rewrite the equation as follows:

V = k/p

where k is the constant of variation.

To find the constant of variation, k, we can use the given information that "When the volume of the gas is 16 cm^3, its pressure is 20 L/cm^2."

16 = k/20

To solve for k, multiply both sides of the equation by 20:

16 * 20 = k

320 = k

Now, we have the constant of variation, k, which is 320.

We can use this value of k to find the volume of the gas when the pressure is 1.6 L/cm^2.

V = 320/p

Substituting the value of p as 1.6 L/cm^2 into the equation:

V = 320/1.6

V = 200 cm^3

Therefore, the volume of the gas when the pressure is 1.6 L/cm^2 is 200 cm^3.

the pressure units are whacked

... pressure is force per unit area ... liters (L) is volume, not force