Question

Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 6L , the pressure is 135 kpa (kilopascals). What is the pressure when the volume is 9L?

Answer 1

The directly proportional relationship between p and q is written as

p ∝ q  where that middle sign is the sign of proportionality. The pressure when the volume is 9L is 90 kPa.

What is a directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p ∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

$m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}$

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

$m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}$

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Boyle's Law says that the volume of a gas varies inversely with the pressure. Therefore, we can write,

Volume ∝ (1/Pressure)

V ∝ (1/P)

V = k/P

When the volume of a certain gas is 6L, the pressure is 135 kPa (kilopascals). Therefore,

6L × 135 kPa = k

k = 810 L-kPa

Now, the pressure when the volume is 9L is,

V = k/P

P = k/V

P = 810 L-kPa / 9L

P = 90 kPa

Hence, the pressure when the volume is 9L is 90 kPa.

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