Physics by Example by Tim Prichard

Author:Tim Prichard
Language: eng
Format: epub
Publisher: Brown Dog Books and The Self-Publishing Partnership

The Gas Laws

Gases are much more complicated than solids and liquids in terms of their behaviour. This is because of the random nature of their movement and the fact they are easily squashed or compressed. If we change either the temperature, volume or pressure of a gas it will affect the conditions of either one or both of the other two factors.

Boyle’s Law

“for a fixed mass of gas, at constant temperature, P × V is a constant”(P = pressure and V = volume)

When doing experiments on gases we find:

If the pressure is doubled the volume is halved, and if the pressure is trebled the volume is reduced to one third of the initial volume.

This means that:

the volume of a gas is inversely proportional to the pressure, which can be expressed as:

P α

Or, more often Boyle’s law is written as:

P1 V1 = P 2 V2

1) A diver is swimming below the surface of the sea and the pressure on the diver is 3.5 atmospheres. At first a bubble of expelled air measures 3 cm 3 in volume. When the bubble reaches the surface of the water the pressure is 1 atmosphere and it pops. Calculate the volume of the bubble just before it popped.

Answer:

Formula: P 1 V1 = P 2 V2

Underwater P = 3.5 atmos and V = 3 cm 3

At the surface P = 1 atmos and V = ?

So P 1 V1 = P 2 V2

3.5 × 3 = 1 V 2

V2 =

= 10.5 cm 3

Note: The bubble has expanded due to the reduction in pressure as it reaches the surface of the water.

2) A balloon is filled with 9.3 litres of gas at a pressure of 3 atmospheres. If the pressure is reduced on the balloon to 0.8 atmospheres, what would the volume of the balloon be now?

Answer:

Formula: P 1 V1 = P 2 V2

Initial

3 × 9.3 = 0.8 × V 2

V2 =

= 34.8 litres

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