Charles' Law: Meaning, Formula, Examples & Applications

Have you ever noticed that a balloon shrinks in winter but expands on a hot summer day? This happens because gases respond to changes in temperature and Charles' Law explains this behaviour.This important gas law forms the foundation of many scientific concepts and has several real-life applications, from weather balloons to vehicle tyres.

The article focuses on Charles' law definition,derivation, graphical representation, everyday examples and practical applications of Charles' Law. 

Table of Contents 

• What is Charles Law
• Charles Law Formula and Derivation
• Applications of Charles Law
• Solved Problems on Charles Law
• Frequently Asked Questions about Charles Law

What is Charles Law

Charles' Law states that the volume of a fixed amount of an ideal gas is directly proportional to its absolute temperature when the pressure remains constant.

In simple words, when a gas is heated, its particles gain kinetic energy and move farther apart. As a result, the gas occupies more space, causing its volume to increase. Similarly, when the gas is cooled, the particles move more slowly, reducing the volume of the gas.

Mathematically,

$V \propto T$

where:

• V = Volume of the gas
• T = Absolute temperature (Kelvin)

This means that if the temperature doubles (in Kelvin), the volume also doubles, provided the pressure and the amount of gas remain unchanged.

Note: Charles' Law is a special case of the Ideal Gas Law and applies only when the pressure and the amount of gas remain constant.

Charles' Law is valid only under the following conditions:

• The pressure of the gas must remain constant.
• The mass or amount of gas should not change.
• The gas should behave like an ideal gas.
• The temperature must always be measured in Kelvin (K) and not in degrees Celsius (°C) or Fahrenheit (°F).

These conditions are important because even a slight change in pressure or the amount of gas can affect the relationship between temperature and volume.

Charles' Law can be observed in many everyday situations where gases expand on heating and contract on cooling.

• Basketballs and footballs feel softer during winter because the air inside contracts as the temperature decreases.
• Car tyres lose pressure on cold mornings and may expand during hot weather due to changes in the volume of air inside.
• Helium balloons shrink in cold environments and regain their size when brought back to a warmer place.
• Pop-up turkey thermometers work because the heated gas inside expands and pushes the indicator upward.
• Hot air balloons rise because the heated air inside becomes less dense and occupies a larger volume.

Also read: Boyles Law 

Charles Law Formula and Derivation 

The mathematical expression of Charles' Law is:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

or

$V_1T_2=V_2T_1$

where:

• V₁ = Initial volume
• T₁ = Initial temperature (Kelvin)
• V₂ = Final volume
• T₂ = Final temperature (Kelvin)

Temperature Conversion

Before applying the formula, always convert Celsius into Kelvin.

K=°C+273K 

For example:

• 25°C = 298 K
• 80°C = 353 K
• 0°C = 273 K

Using Kelvin ensures accurate calculations because Charles' Law is based on the absolute temperature scale.

Derivation of Charles' Law

Charles' Law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature at constant pressure.

Therefore,

According to Charles' Law,

$[ V \propto T ]$

Introducing the proportionality constant k,

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

For the initial state of the gas,

$[ \frac{V_1}{T_1}=k ]$

After the temperature changes,

$[ \frac{V_2}{T_2}=k ]$

Since both equations are equal to the same constant k,

$[ \frac{V_1}{T_1}=\frac{V_2}{T_2} ]$

Cross-multiplying,

$[ V_1T_2=V_2T_1 ]$

This is the mathematical expression of Charles' Law, showing that the volume of a fixed amount of gas is directly proportional to its absolute temperature when the pressure remains constant.

This equation is known as the Charles' Law equation and is used to calculate the unknown volume or temperature of a gas when pressure remains constant.

Absolute Zero and Charles' Law

One interesting concept related to Charles' Law is absolute zero.Absolute zero is the lowest possible temperature, equal to:

• 0 K
• -273.15°C

At this temperature, the volume of an ideal gas theoretically becomes zero because the gas particles possess minimum kinetic energy.

Graphical Representation of Charles' Law

The graph between volume (V) and temperature (T) at constant pressure is called an isobar.

Characteristics of the Graph

• The graph between Volume (V) and Temperature (K) is a straight line passing through the origin, showing a direct proportional relationship.
• When temperature is plotted in degrees Celsius, the straight line intersects the temperature axis at -273.15°C, which represents absolute zero.
• The graph clearly shows that increasing temperature increases the volume of the gas, while decreasing temperature reduces its volume.

This graphical representation helps students understand why gases expand on heating and contract on cooling.

Relationship Between Temperature and Density

Charles' Law also explains the relationship between temperature and density.

Since the mass of the gas remains constant,

• Increasing the temperature increases the volume.
• As volume increases, the density decreases.
• Therefore, the density of a gas is inversely proportional to its absolute temperature when pressure remains constant.

This concept explains why hot air is less dense than cold air and rises upward.

Applications of Charles Law

Charles' Law has several practical applications in science and everyday life.

• It explains the working of hot air balloons.
• It helps in designing weather balloons that expand as they rise into colder atmospheric layers.
• It is used in internal combustion engines, where heated gases expand to produce mechanical work.
• It helps understand seasonal changes in tyre pressure.
• It explains why human lung capacity decreases in cold weather, making physical activities like running more difficult. 

Solved Problems on Charles Law

Example 1

A gas occupies 400 cm³ at 0°C. Find its volume at 80°C if the pressure remains constant.

Given:

$V_1 = 400\ \text{cm}^3$

$T_1 = 0^\circ\text{C} = 273\ \text{K}$

$T_2 = 80^\circ\text{C} = 353\ \text{K}$

 Using Charles' Law,  $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Substituting the values,  $\frac{400}{273}=\frac{V_2}{353}$

$V_2=\frac{400\times353}{273}$

$[ V_2=517.2\ \text{cm}^3 ]$

Since,  $[ 1\ \text{cm}^3 = 0.001\ \text{L} ] [ 517.2\ \text{cm}^3 = 0.517\ \text{L} ]$

Answer:  $\boxed{V_2=517.2\ \text{cm}^3=0.517\ \text{L}}$

Example 2

A gas occupies 30.8 L at -67°C. If its volume decreases to 21.0 L, find the new temperature.

Answer:

Using Charles' Law,

$T2=21×20630.8≈140$

$KT_2=\frac{21\times206}{30.8}\approx140\$

$KT2=30.821×206≈140 K$

Converting to Celsius,

$140-273=-133^\circ C$

Answer:140 K (-133°C)

Note: The competitor solution shows 46.9°C, but that calculation is incorrect. The correct answer is approximately -133°C.

Common Mistakes to Avoid

• Using Celsius instead of Kelvin.
• Applying Charles' Law when pressure is changing.
• Forgetting to convert the final answer into the required unit.
• Mixing different volume units without conversion.

Read more: Avogadro’s Law and Graham's Law

We have learned that Charles' Law explains the relationship between the volume and temperature of a gas at constant pressure, making it one of the most important gas laws in chemistry. It helps students understand why gases expand when heated and contract when cooled and its principles are widely used in everyday life, from hot air balloons to vehicle tyres and weather balloons.