The volume V of a gas varies directly with the reciprocal of the pressure P. What happens to the volume of the gas if the pressure is tripled?

V = k * (1/P)

So what happens to V if you triple the value of P?

Thank you yur soooo helpful!!!

wait a sec but a still don't get it.

To understand what happens to the volume of the gas when the pressure is tripled, we can use the concept of direct variation.

Direct variation states that two variables are directly proportional to each other if their ratio remains constant. In this case, the volume V of the gas varies directly with the reciprocal of the pressure P, which can be mathematically represented as:

V ∝ 1/P

To find out what happens to the volume when the pressure is tripled, we can set up a proportion by comparing the initial condition to the new condition:

V1 ∝ 1/P1
V2 ∝ 1/P2

Where V1 is the initial volume, P1 is the initial pressure, V2 is the new volume, and P2 is the new pressure.

Let's assume the initial pressure is P1, and the new pressure is tripled, which means P2 = 3P1.

Now, substituting the values into the proportion, we get:

V1 ∝ 1/P1
V2 ∝ 1/(3P1)

To find the relationship between V2 and V1, we can divide V2 by V1:

V2/V1 = (1/(3P1)) / (1/P1)
V2/V1 = (1/(3P1))*(P1/1)
V2/V1 = 1/3

Therefore, when the pressure is tripled, the volume of the gas becomes one-third of its initial volume. In other words, the volume decreases by a factor of three.