Question

Help!

The pressure, P, of a gas varies inversely with its volume, V. Pressure is measured in units of Pa. Suppose that a particular amount of a gas is initially at a pressure of 84 Pa at a volume of 51 L. If the volume is expanded to 153 L, what will the new pressure be?

Answer 1

P = k/V

84 = k/51
4,284 = k

P = 4,284 / 153
P = 28Pa

Hope I helped!

Answer 2

Inverse variation states:

If
`y \propto (1)/(x)`

then the equation is in the form of :

`y = (k)/(x)`

where, k is the constant of variation.

As per the statement:

The pressure, P, of a gas varies inversely with its volume, V

By inverse variation definition;

`P= (k)/(V)` ....[1]

It is also given that a particular amount of a gas is initially at a pressure of 84 Pa at a volume of 51 L

⇒P = 84 Pa and V = 51 L

then;

`84= (k)/(51)`

⇒
`k=84 \cdot 51=4284`

If the volume(V) is expanded to 153 L then find the new pressure.

Using [1] we have;

`P= (4284)/(153) =28` Pa

Therefore, the new pressure be , 128 Pa