# To measure the coefficient of expansion of a gas at constant pressure: Charles's law

 Charles's law
One of the several different forms of apparatus available for this experiment is illustrated in the image.
A quantity of dry air is contained in a glass bulb B, which forms part of a U-tube graduated to read volume in cm³. A straight tube leading from the bend of the U-tube is connected to a mercury reservoir by a length of rubber tubing. The temperature of the air is controlled by a water bath which may be heated either by an electric immersion heater or else by passing in steam.
 Charles's law apparatus
Now, dry air is introduced into the apparatus by the same method as that used for the Boyle's law apparatus. Starting with cold water in the bath, the reservoir is adjusted until the mercury levels in both sides of the U-tube are the same. The enclosed air will then be at atmospheric pressure.
Having noted the volume of the air and the temperature, the water is then stirred continuously and its temperature raised in steps of about 10 degrees at a time.
At each stage the reservoir is adjusted to equalize the mercury levels and the volume and temperature recorded, after allowing sufficient time for the air to acquire the temperature of the water.
Provided the atmospheric pressure remains constant, the change in volume of the air will be due to temperature only. The expansion of the glass introduces a slight error, but owing to the fact that this is small compared with the expansion of the air it may be neglected.
From the results obtained, a graph of volume against temperature is plotted. The graph is found to be practically a straight line, showing that the air expands uniformly with temperature as measured on the mercury thermometer.
If the graph is produced backwards it cuts the volume axis at a point which gives the volume which the air would have at 0°C. Similarly, by producing the graph in the opposite direction the volume of the air at temperatures of 100°C or more may be obtained. Producing a graph in this way is called extrapolation

## To calculate the volume coefficient of expansion

The simplest way of calculation the volume coefficient of expansion, α, is to read from the graph the volumes of the air V0 and V100 at 0°C and 100°C respectively and to substitute in the equation,
α =change in volume / volume at 0°C × change in temperature

i.e.  α = V100 - V0 / V0 × 100 per °C
 charles's law graph
The value obtained is approximately 1/273 or 0.00366/°C and, moreover, practically the same result is obtained for all gases.

### Balloons and Charles's law

The original experimental work on this subject was carried out towards the end of the eighteenth century by the distinguished French scientist, Jacques Charles, whose researches were doubtless inspired by an interest in flight by hot-air balloons. He later decided in favor of hydrogen balloons, since these had greater lifting power.
The results obtained in the experiment just described is generally known as Charles's law.