# Boyle's law and charle's law

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Charles' Law

The volume of an enclosed sample of gas is directly proportional to its absolute temperature provided the pressure is kept constant.

## Interesting fact

Charles's Law is also known as Gay-Lussac's Law. Charles did not publish his work. Gay-Lussac later rediscovered this law and referenced Charles's work, but said that it was only by great luck that he knew of it and that his experiment was different.

## Demonstration : charles's law

Aim:

To demonstrate Charles's Law using simple materials.

Apparatus:

glass bottle (e.g. empty glass coke bottle), balloon, bunsen burner, retort stand

Method:

1. Place the balloon over the opening of the empty bottle.
2. Place the bottle on the retort stand over the bunsen burner and allow it to heat up. Observe what happens to the balloon. WARNING: Be careful when handling the heated bottle. You may need to wear gloves for protection.

Results:

You should see that the balloon starts to expand. As the air inside the bottle is heated, the pressure also increases, causing the volume to increase. Since the volume of the glass bottle can't increase, the air moves into the balloon, causing it to expand.

Conclusion:

The temperature and volume of the gas are directly related to each other. As one increases, so does the other.

Mathematically, the relationship between temperature and pressure can be represented as follows:

$V\propto T$

or

$V=kT$

If the equation is rearranged, then...

$\frac{V}{T}=k$

and, following the same logic that was used for Boyle's law:

$\frac{{V}_{1}}{{T}_{1}}=\frac{{V}_{2}}{{T}_{2}}$

The equation relating volume and temperature produces a straight line graph (refer back to the notes on proportionality if this is unclear). This relationship is shown in [link] .

However, if this graph is plotted on a celsius temperature scale, the zero point of temperature doesn't correspond to the zero point of volume. When the volume is zero, the temperature is actually -273.15 ${}^{\circ }$ C ( [link] ).

A new temperature scale, the Kelvin scale must be used instead. Since zero on the Celsius scale corresponds with a Kelvin temperature of -273.15 ${}^{\circ }$ C, it can be said that:

Kelvin temperature (T) = Celsius temperature (t) + 273.15

At school level, you can simplify this slightly and convert between the two temperature scales as follows:

T = t + 273

or

t = T - 273

Can you explain Charles' law in terms of the kinetic theory of gases? When the temperature of a gas increases, so does the average speed of its molecules. The molecules collide with the walls of the container more often and with greater impact. These collisions will push back the walls, so that the gas occupies a greater volume than it did at the start. We saw this in the first demonstration. Because the glass bottle couldn't expand, the gas pushed out the balloon instead.

## Charles's law

The table below gives the temperature (in ${}^{\circ }$ C) of a number of gases under different volumes at a constant pressure.

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