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# Charles's Law- Statement, Representation, Application, Practice problems and FAQs

Have you ever wondered why tyres burst sometimes on hot summer day? Well, It is due to the fact that during a hot summer day temperature is higher which results in an increase in the volume of the gas inside tyre and the tyre expands and ultimately it bursts. Jacques Charles explained the relationship between the volume of the gas and temperature in the form of a law known as Charles’s law.

Table of content

• Statement of Charles’s Law
• Mathematical representation of Charles’s law
• Graphical representation of Charles’s law
• Application of Charles’s law
• Practice problems

## Statement of Charles’s law

According to Charles’s law “ for a fixed amount of a gas at constant pressure, the volume of a gas increases by times of the original volume of the gas at with every one-degree rise in the temperature.

Alternatively, it can also be written that “volume occupied by a fixed amount of gas at constant pressure is directly proportional to its temperature (in its absolute scale, )”.

## Mathematical representation of Charles’s law

Let us assume;

Initial volume of the gas at

Final volume of the gas

Initial temperature of the gas

Increase in temperature of the gas (Considering, )

Final temperature of the gas

According to Charles’s law,

Increase in the volume of gas per degree rise in temperature

Increase in the volume of the gas at

Final volume of gas Initial volume + Increase in the volume of the gas

Substituting and in the equation we get,

(∵ and are constants)

Where represents the proportionality constant, represents the volume occupied by the gas at temperature , represents the temperature in the Kelvin scale.

Now, consider two different conditions of the same gas. The volume and temperature of the gas is changed keeping the pressure and amount of the gas constant.

Let’s assume;

Initial volume of the gas

Initial temperature of the gas

Final volume of the gas

Final temperature of the gas

According to Charles’s law equation;

Putting the two values separately in the equation we get,

Using equations and we get;

Note: Temperature should be kept in kelvin while solving numericals.

## Graphical representation of Charles’s law

The curve for a fixed amount of gas and at constant pressure is represented as;

We know the general equation of a straight line is

Where, and represent the co-ordinate axis, represents the slope of the curve and represents the intercept on axis.

Now, according to Charles’s law,

If we compare the equation and , we can say;

Intercept and Solpe

Therefore, the above curve between volume and temperature is a straight line with a constant slope and if this straight line is extrapolated it will pass through the origin.

Let us see one more plot between Volume and Temperature where several curves are given a different pressures.

Now, let's focus on the points on those three straight lines where the temperature is fixed.

Now, as you can see from the plot:

According to the Boyles law,

(at constant temperature)

Here, in this case, we are talking about a constant temperature .

So, it can be concluded from the Boyle’s law and above graph that:

The Volume and Temperature ) curve for a fixed amount of gas and at a constant pressure can be represented as:

According to Charles’s law;

If we compare equation with the straight line equation

We can say that and Slope

At , the volume occupied by the gas is assumed to be and the temperature is known as absolute zero.

## Application of Charles’s law:

Charles's law has a wide range of applications which includes:

• Hot air balloons
• Fluffiness of the bakery products
• Bursting of a deodorant bottle
• Restoring shape of dented Ping-Pong ball

## Practice problems

Q1. To what temperature must an ideal gas be heated at a constant pressure to increase the volume of the gas from ?

Solution: As per the given data;

Initial volume of the gas

Initial temperature of the gas

Final volume of the gas

Final temperature of the gas

According to Charles's law;

Q2.  of a gas occupies the volume of at temperature and pressure. What will be the temperature of the gas when the volume gets doubled keeping the pressure same?

Solution: As per the given data;

Initial volume of the gas

Initial temperature of the gas

Final volume of the gas

Final temperature of the gas

According to Charles's law,

Putting the values in the above equation;

Q3. If a gas is cooled down from to and gas occupies a volume of at . Calculate the initial volume of a gas. Assuming pressure is kept constant and the amount of gas is fixed.

Solution: Given;

Initial volume of the gas

Initial temperature of the gas

Final volume of the gas

Final temperature of the gas

According to Charles’s law,

Q4. Which of the following is correct with respect to Charles’s law?

1. It shows the volume-temperature relationship for a fixed amount of gas
2. It shows volume- temperature relationship for a fixed amount of a gas at constant pressure
3. It shows the pressure-temperature relationship at constant volume and for a fixed amount of gas
4. It shows the pressure-volume relationship for a fixed amount of gas

Solution: According to Charles law “volume occupied by a fixed amount of gas at constant pressure is directly proportional to its temperature”.

Q1. What happens to the matter at absolute zero temperature?

Answer: The zero on a kelvin scale is called absolute zero temperature. It corresponds to. At absolute zero temperature movement of the molecules ceases and the volume occupied by the gas is assumed to be .

Q2. What is the significance of Charles’s law in bakery products?

Answer: Yeast is generally used for making bakery products fluffy by releasing carbon dioxide gas. According to Charles’s law, volume of the gas is directly proportional to temperature. Carbon dioxide gas expands when heated and gets released from the bakery product and acts as a leaving agent making bakery products fluffy.

Q3. How can the relationship between the density of gas and temperature be explained using Charles's law?

Answer: According to Charles’s law, we know that volume of the gas and temperature are directly proportional considering pressure and amount of gas to be constant.

Density of the gas

Since the amount of gas is assumed to be constant.

Therefore, Density of the gas

According to Charles’s law,

Volume of the gas Temperature

So, considering , it can be said that;

Density of the gas is inversely proportional to the temperature of the gas.

Q4. What happens when the tube is overfilled and placed in a pool on hot summer days?

Answer: During hot summer days when the tube is overfilled and placed in a pool it gets heated by the sunlight. We know, according to Charles’s law, the volume of the gas is directly proportional to its temperature. Therefore, it swells up and bursts.

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