# What is the Charle’s Law of Gases? Definition, Formula, Graph, Equation, Examples

In this article, we will learn what is Charle’s law of Gases, definition, formula, graph, equation, examples, etc.

Let’s explore!

## What is the Charle’s Law of Gases?

### Charle’s Law of Gases Basics

Before getting to Charle’s Law, let’s try to understand what are Gas laws?

A set of laws was developed to understand the nature and behavior of gas and to establish a relationship between

• The volume of gas particles
• The pressure acting on the gas particles
• Heat energy possessed by the gas molecules
• Number of moles of gas

But the study of gases is quite complicated, and it is difficult to establish any kind of relation between the above-mentioned properties. So, scientists created the concept of an ideal gas which would be a close approximation of the real gas.

This way we are provided with a model with the help of which behavior of real gases can be predicted and understood.

### Conditions which describe an Ideal Gas

Ideal gas molecules don’t attract or repel one another. They continuously move in random motion and only change direction when they collide with other gas molecules.

All collisions with other gas molecules as well as walls of the container are completely elastic.

When compared to the total volume filled by the entire gas, the volume of each gas molecule is negligible.

Ideal gases are governed by an Ideal Gas Equation which is given as:

P V = n R T

Where,

• P= Pressure exerted on the gas
• V= Total volume of the gas
• n= number of moles of gas
• R= 8.3143 J / mol-Kelvin
• T= Temperature in Kelvin

There are four basic gas laws each derived as a special case of Ideal Gas Equation which is as follows:

• Charles’s Law
• Boyles’s Law
• Gay-Lussac’s Law

## Charle’s Law of Gases & Statement

### Charle’s Law of Gases

Jacques Charles, a French inventor, scientist, and mathematician is credited for launching the first unmanned hydrogen-filled gas balloon in August 1783 and then later that year in December, a manned flight in the hydrogen-powered gas balloon which ascended a height of 1800 feet.

Around 1787, Jacques Charles performed an experiment to understand the relationship between volume and temperature of gases. He filled five balloons with five different gases but to the same volume at room temperature. The five balloons were then subjected to heat to increase their temperatures to 800C. An increase in temperature caused the gases to expand and it was observed that all five balloons increased in volume by the same amount.

The law that is used to explain the effect on the volume of gas due to temperature under constant pressure is called Charles’s Law.

### Charle’s Law of Gases Statement

Charles Law states that the total volume occupied by gas particles is directly proportional to the absolute temperature (Kelvin temperature) of the gas under the condition that the pressure acting on the gas remains constant.

Let’s take an example,

Consider a balloon filled with air. The balloon is completely isolated from the surroundings and hence no air enters the balloon (system) and no air exits the balloon (system).

For convenience, we consider that there are exactly 100 particles of air in the balloon and due to the isolated nature of the system, the number of particles remains constant throughout.

At any given point in time, these particles keep moving at a certain velocity in a random direction and keep colliding with each other.

Now, start heating this container. By heating, their velocity increases, and the frequency of collision of particles increases. This increases the total volume occupied by the gas but keep in mind that the number of particles is still the same. So the same number of molecules are now occupying more areas inside the container.

But the law also states that all of these has to take place at constant pressure condition. So what does that mean?

Now, as the gas expands inside the container, the walls of the balloon also expand. This allows for constant pressure to be maintained on the gas particles. If instead of a balloon we had a solid container then expansion of gas would have been restricted by the walls of the container thereby increasing pressure.

This is however a hypothetical balloon as it is not possible to produce a system that can completely isolate itself from the surrounding.

Thus, the hypothetical system exerts constant pressure on the gas particles, and under this condition, the total volume occupied is directly proportional to the absolute temperature of the gas.

## Derivation of Charle’s Law of Gases Formula & Equation

### How to Derive Charle’s Law of Gases?

The above experiment was carried out in an ideal condition and has the equation governing it is derived from the ideal gas equation.

P V = n R T

Now, from the gas equation

• V  =  nRT/P

The number of molecules (n) was kept constant throughout the process by isolating the system and surroundings.

R has a constant value as we know.

The pressure exerted by the system on the gas was also kept constant.

Therefore,

• V = k T

where, k = constant of proportionality

So, we get,

• V/T = constant = k

Let V1 and T1 be the initial volume and temperature of an ideal gas,

• V1/T1  = k      ——— 

Let V2 and T2  be the final volume and temperature of an ideal gas,

•  V2/T2 = k      ——— 

Hence from both equations  and  we get,

• V1/T1 = V2/T2 =  k
• V1 T2 = V2 T1

This becomes the mathematical representation of Charles Law. The relationship holds true only when the temperature is expressed in Kelvin. (1 Kelvin = 273 + 1oC )

## Limitation of Charle’s Law of Gases

As we discussed, Charles’s Law states that the total volume and absolute temperature of the gas are directly proportional under the conditions of constant pressure. So that would mean that when the absolute temperature starts dropping, the total volume occupied by the gas also starts reducing.

Theoretically, we should arrive at a temperature to which the corresponding volume is zero. But something like that is not practically possible as cooling the gases below their saturation point causes the gases to condense into liquids. Once the gases convert into liquid, conditions of Charles’s law do not apply to it.

Hence it can be concluded that Charles Law does not apply to gases at lower temperatures or temperatures below the saturation point of the gases.

Let’s explore Charles’s Law and Kinetic Theory of Gases

## Charles’s Law and Kinetic Theory of Gases

The kinetic theory of gases also explains the relationship between absolute temperature and the total volume of gas at constant pressure. However, it is not a different approach rather it provides a much deeper explanation as to why volume increases when the temperature of gas increases.

When the gas is kept inside a balloon the gas molecules exert a certain amount of pressure on the walls. As you increase the temperature of the gas, the kinetic energy of the gas increases which also increases the frequency of collision. This results in more amount of pressure acting on the gas particles.

The gas has to expand so that the molecules are further away from each other and the collision of gas particles against the walls reduces thereby reducing pressure acting on the gas particles.

However, the pressure will not reduce if the walls of the balloon do not allow for an increase in the volume of gas.

Thus, to summarize, both the velocity and frequency of collision increase with a rise in the temperature. The volume of space occupied by the gas must increase so that pressure acting on the gas particles can be maintained constant.

## Absolute Zero Temperature

With reference to the kinetic theory of gases, the kinetic energy of the gas particles is directly proportional to the temperature of the gas. High kinetic energy causes the velocity of gas particles to increase and due to that the frequency of collision of gas particles with other gas particles and walls of the container increases.

So basically, the higher the temperature, the greater will be the kinetic energy of the particles and the more will be the frequency of collision.

Similarly, as the temperature drops the kinetic energy of the particle also drops and this causes the particles to slow down.

If this continues then there comes a point where the particles eventually stop moving at all. At this point, the particles have lost all of their energy and are now at a complete standstill eliminating any kind of interaction.

This temperature at which the particles become completely motionless is called Absolute Zero Temperature. There is no way to slow down the particles any further and hence a temperature lower than this cannot be achieved.

Absolute Zero Temperature value is equal to 0 degree Kelvin.

Thus theoretically, at absolute zero temperature, the total volume of an ideal gas would become zero and all particle motion would cease to exist.

Practically, however, the gases condense to liquid or turn to solid as the temperature falls below their saturation temperature which is well above absolute zero temperature.

Hence, Charles’s law is just an approximation to real gas behavior.

## Experiment to Determine the Value of Absolute Zero Temperature in Degree Celsius

A gas is placed inside an isolated container and under the influence of a movable piston. The piston creates a constant force on the gas.

Note down the initial temperature and volume of gas. Now start providing heat to the gas. This will cause the gas to expand. Do this for several values of temperature and volume.

Once the experiment is done, plot a graph using the obtained values between volume and temperature with the volume on the y-axis and temperature on the x-axis.

The curve will start well above and ahead of the x-axis and y-axis respectively. This is because the gases will remain in a gaseous state only above a specific temperature, which we call boiling point.

Method#1

Use the formula,

y = mx + c

Where,

• y = value on y axis
• x = value on x axis
• m = slope of the curve
• c = y-intercept

You need to find the y-intercept for the curve i.e., the point where the curve intersects the y-axis. Do this by extending the curve all the way to the y-axis. The point where it intersects the y-axis gives us a y-intercept. Let that value be c in the above formula.

For absolute zero temperature put y=0 because we have to find the x coordinate

Calculate the slope and substitute for m.

The value of x co-ordinate comes out to be approximately -273 oC.

Method#2

This method is relatively very simple.

Extend the curve until it intersects with the x-axis and that gives the absolute zero temperature which would approximately be -273 o C.

## Charles’s Law Graph

From the definition & statement of Charle’s Law, we can see the graphical representation of this law.

• We know,
• V = kT or
• y = mx

It means simply a straight line. Here, volume is directly proportional to the temperature when the temperature is constant.

## Examples of Charles’s Law in Real Life

• Hot air balloons are first filled with air inside it followed by which the air is then heated. As the temperature of the air rises, the kinetic energy of air increases and air expands. Now as the volume of air increases, its density decreases compared to the air outside. This difference in densities of air causes the hot air balloon to rise up in the air.
• Air / Fuel mixture enters the combustion chamber of an internal combustion engine. This mixture is then compressed by the upward motion of the piston from BDC to TDC. Just as the mixture is sufficiently compressed and the piston reaches TDC, heat is introduced to the mixture via spark plug which causes spontaneous ignition of air/fuel mixture. This causes the gas inside the combustion chamber to expand pushing the piston downwards to BDC. This way chemical energy of the fuel is converted to mechanical energy which enables the vehicle to move.
• Deodorant bottles contain pressurized gas inside it. Exposing it to heat can cause the container to rupture due to the expansion of gas particles inside it. Hence it is advised to keep it away from heat.
• When a balloon completely filled with air is exposed to a cold surrounding, the balloon crumbles and falls on the floor. The reason behind this is that as the temperature of gas particles reduces, their kinetic energy reduces. This in turn results in a reduction in velocity of gas particles as well as in the frequency of collision. To compensate for the reduction in pressure gas particles move closer reducing the volume occupied by the gas. With reducing volume, the density of the air inside the balloon increases and causes the balloon to crumble to the ground.

## Conclusion

Hence, we have learned what is Charle’s law of Gases, definition, formula, graph, equation, examples, etc. along with detailed explanations.

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