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# Gay-Lussac’s Law- Statement, Representation, Application, Practice problems and FAQs

Have you ever wondered why in some aerosol bottles like deodorant bottles warning instructions are written on the backside mentioning “keep it in a cool place away from heat and sunlight”? Yes! It is due to the fact that there is some relation between the pressure and temperature. In 1808, French chemist Joseph Gay-Lussac explained the relationship between the pressure exerted by the gas and temperature in the form of a law known as Gay-Lussac’s law.

Table of content

• Statement of Gay-Lussac’s Law
• Mathematical representation of Gay-Lussac’s law
• Graphical representation of Gay-Lussac’s law
• Applications of Gay-Lussac’s law
• Practice problems

## Statement of Gay-Lussac’s law

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

Alternatively, Gay-Lussac’s law can be stated as “at constant volume and for a fixed amount of gas, the pressure of the gas is directly proportional to its temperature (in Kelvin scale)”

## Mathematical representation of Gay-Lussac’s law

Let us assume;

Initial pressure of the gas at

Final pressure of the gas

Initial temperature of the gas

Increase in temperature of the gas (Considering, )

Final temperature of the gas

According to Gay-Lussac’s law,

Increase in the pressure of gas per degree rise in temperature

Increase in the pressure of the gas at

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

Substituting and in the equation we get,

(∵ and are constants)

Where represents the proportionality constant, represents the pressure exerted by the gas at temperature , represents the temperature in the Kelvin scale.

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

Let’s assume;

Initial pressure of the gas

Initial temperature of the gas

Final pressure of the gas

Final temperature of the gas

According to Gay-Lussac’s law,

Putting the two values separately in the equation we get,

From equation and , we get,

Constant

Where represent pressure exerted by the gas and represent the absolute temperature of the gas in Case and Case respectively.

Note: Temperature should always be kept in Kelvin scale while solving the numerical.

## Graphical representation of Gay-Lussac’s law

The curve for a fixed amount of gas and at constant volume 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 Gay-Lussac’s law,

If we compare the equation , we can say;

Intercept and Solpe

Therefore, the above curve between pressure 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 Pressure and Temperature where several curves are given at different volumes.

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 Boyle's 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:

## Application of Gay-Lussac’s law

Gay-Lussac’s law has a wide range of applications which includes:

• Bursting of the tyre during hot summer days
• Working of a pressure cooker
• Bursting of aerosol cans when subjected to heat

## Practice problems

Q 1. A sample of an ideal gas is taken in a flask at an initial pressure of . What will be the final pressure of the gas when it is cooled from

Answer: According to the given data;

Initial pressure of the gas

Initial temperature =

Final pressure of the gas

Final temperature =

According to Gay- Lussac’s law,

Q 2. If an ideal gas is taken in a closed container at an initial pressure of and a temperature of . Calculate the final temperature of the gas in when the gas is pressurised to .

Answer: According to the given data;

Initial pressure of the gas

Initial temperature

Final pressure of the gas

Final temperature

According to Gay- Lussac’s law,

Q 3. The pressure exerted by of an ideal gas at a temperature in a vessel of volume is . When the temperature is increased by degrees at the same volume, pressure increases by . Calculate the temperature in degrees celsius.

(Molecular weight of the gas )

Answer: According to the given data;

Initial pressure of the gas

Initial temperature of an ideal gas

Final pressure of the gas Initial pressure Increase in the pressure

Initial temperature of an ideal gas

According to Gay- Lussac’s law,

Q 4. For the plot given below, pressure is related to temperature in the following way:

where is to be measured in and is to be measured in .

The slope of the curve given in the plot of is:

a.
b.
c.
d.

According to the given data;

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 the equation given in the question;

If we compare these two equations, we can say;

Intercept and Solpe

According to Gay-Lussac’s law,

If we compare equation and we get;

Q 1.What will happen when an aerosol bottle like a deodorant bottle will be exposed to heat?
Answer: When an aerosol bottle like a deodorant bottle is exposed to heat the pressure inside the bottle increases due to an increase in the temperature as per Gay-Lussac’s law and once the threshold is reached it gets exploded. To prevent this it is recommended to keep the aerosol bottles away from the heat.

Q 2. What is the significance of Gay- Lussac’s law in firing a bullet?