Question

Under a pressure of 14Nm-2, some air has

a volume of 1.5m3. Determine its volume
when its pressure is 10Nm-2. Assuming the
temperature is kept constant

Answer 1

2.1 m³

Step-by-step explanation:

Boyle's Law states:
The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system (Wikipedia) }

We can express this relationship as

`P \propto (1)/(V)`

where V is the volume under pressure P

This can be re-written as:
PV = a constant

We are given that
`$V = 1.5m^3$` when
`$P = 14N/m^2$`

So PV = 1.5 x 14 = 21 Nm

At
`10 N/m^2` the PV product must also be 21

So 10V' = 21 where V' = volume at
`\displaystyle 10 N/m^2`

Therefore V' = 21/10 = 2.1 m³