Charles’s law explains how gases expand when they are heated. This law is also known as the law of volume. It is because the volume has a direct relationship to the temperature of gases such that, an increase in temperature causes an increase in their volume as well.

Charles states that:

At constant pressure, the volume of the fixed mass of an ideal gas is directly proportional to the degree of absolute temperature. If the absolute temperature is doubled, the volume of the gas doubles too”. Outline

## History of Charles’s law

Charles’s law was introduced by Jacques Charles in 1787. Later, it was published by Joseph Louis Gay Lussac in 1802. The basic principle of the law was actually described by the two scientists earlier than these two; Guillaume Amontons in 1702 and Francis Hauksbee in 1705.

The work on expansion and partial pressures of gases was started by Alchemy which was carried on by Antoine Lavoisier, and later on by John Dalton. In 1702, Guillaume Amontons suggested that there may be a state of absolute zero, later taken up by Kelvin.

The contribution of Dalton to Charles’s law is the application of this law to all gases and vapors of volatile liquids. Dalton and Gay Lussac’s conclusion can be expressed by equation.

V100 – V0 = kV0

where,

• V100 = volume of the sample gas at 100 oC
• V0 = volume of the gas at 0 oC
• k = constant

## Mathematical Derivation of Charles’s law

According to Charles’s Law, the volume of gas is directly proportional to its absolute temperature at constant pressure.

It can be expressed mathematically as;

V ∝ T

Or

V = kT

where,

• V is the volume of gas
• T is the temperature of the gas
• k is the constant of proportionality

This equation can be interchanged to:

V / T = k

If V1 and T1 are the initial volume and temperature of a sample gas at constant pressure and V2 and T2 are the final ones, this law can be written as:

V1 / T1 = k = V2 / T2

V1 / T1 =  V2 / T2  (Charles’s law)

By using the above equation, a rather impossible new volume (V2) can be found from the experimental values of V1, T1, and T2.

## Graphical Presentation of Charles’s Law

This graph shows that at constant pressure, the volume of the given sample of the gas is directly proportional to the kelvin temperature. ### Relationship with Absolute Zero

In 1852, Thomson described that absolute zero on the Kelvin scale can be explained by the second law of thermodynamics which later on in around 1870 had become the new basis to define the entropy of the system.

Charles stated that;

For every 1 degree rise in the temperature of a gas, its volume increases by 1/273 of its volume at 0 degrees celsius. This new relation was given by:

VT = V0 + (1/273 x V0) x T

VT = V0 + (1 + T/273)

• VT is the volume of sample gas at temperature (T).
• V0 is the volume of gas at 0oC temperature.

### An Ideal thermometer

It is the thermometer that can measure the internal energy of a substance without any reference. For example, the Kelvin scale is designed on the principle of Charles law. By decreasing the temperature of a gas, its volume will also decrease. The temperature at which the volume of that gas becomes zero is -273.16 °C. It is also known as absolute zero point because it equals 0 °K.  On a graph, it is found by extrapolating the graph back into the negative temperature axis, as shown above.

## Applications of Charles’s Law

Charles’s law is one of the basic and fundamental gas laws. Obviously, it is applicable only to ideal gases, but with few arrangements, it can theoretically be applied to real gases. Some applications of Charles’s law are:

• Ideal thermometer
• Absolute zero
• A flying hot air balloon
• Shrinking of a car tire in the winter season
• Reduction of the gap between railway lines on cold days
• Blasting of balloons on hot days
• Expansion of metals (linear and volumetric thermal expansion) with increasing temperature
• Bakery applications (CO2 expands at high temperatures and makes baking possible), etc

## Concepts Berg

What is Charles’ law application in real life?

A hot air balloon is used for advertisements, expansion of bakery items with yeast, brushing tires in summers, etc are some examples of Charles’s law.

What Happens at absolute zero?

At absolute zero, all types of energies become zero. This is an ideal situation that does not exist in real life.

Why temperature must be Kelvin?

Kelvin’s temperature scale is the most accurate of all. The reason is that it is an absolute scale. Therefore, it has minimum errors.

Is the Kelvin scale derived from Charles’s law?

Yes, the Kelvin scale is derived from Charles’s law.

Who introduced Charles’s law?

Gay Lussac introduced Charles’s law. Charles was gay’s mentor, so, he referred it to his name.

References

• Chemistry The Practical Science By Paul B. Kelter, Michael D. Mosher, and Andrew Scott
• The Fundamentals of Nuclear Power Generation: Questions & Answers By M. W. Hubbell