Gay Lussac’s Law: Formula, Derivation & Real-life Examples

Gay Lussac’s law states that pressure exerted by any gas with a given mass and at a constant volume directly varies with absolute gas temperature. Simply saying, the pressure exerted by a gas is directly proportional to its absolute temperature when kept at constant mass and volume. A French chemist Joseph Gay-Lussac formulated this law in 1808. Gay-Lussac’s law is one of the most important gas laws that eventually paved way for the ideal gas law equation.

What is Gay Lussac’s Law?

Gay Lussac’s law states that the pressure exerted by a gas is directly proportional to its absolute temperature when kept at constant mass and volume. Gay Lussac’s law can be mathematically represented as,

P α T

→ P/T = K

Here,

P → Pressure being exerted by the gas

T → Absolute temperature of the gas

K → constant

Gay Lussac’s Law

The relationship between the absolute temperature of gas and pressure exerted by it at constant mass and volume is mentioned in the diagram below.

Relation between temperature and pressure

In the diagram above, the pressure exerted by a gas increases constantly with an increase in temperature and decreases with a decrease in temperature.

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Formula and Derivation of Gay Lussac’s Law

According to Gay Lussac’s Law, the ratio of initial pressure and temperature is equal to the final pressure and temperature of a gas at constant mass and volume.

The formula of Gay Lussac’s Law is:

(P₁/T₁) = (P₂/T₂)

Here,

P₁ → Initial pressure of the gas

T₁ → Initial temperature of the gas

P₂ → Final pressure of the gas

T₂ → Final pressure of the gas

This expression is derived from the temperature and pressure proportionality of gas. Gay Lussac’s law says that pressure is directly proportional to temperature kept at fixed mass and constant volume. 

P₁/T₁ = k (Ratio of Initial pressure and temperature)

P₂/T₂ = k (Ratio of final pressure and temperature)

Therefore, 

P₁/T₁ = P₂/T₂ = k

Or, 

P₁T₂ = P₂T₁

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Examples of Gay-Lussac’s Law

A pressurised gas like an aerosol can of deodorant or spray paint when heated results in an increase in the pressure exerted by a gas on the container walls that can result in an explosion. This is the main reason for which pressurised gas containers have been warned to be kept in a cool environment and away from fire.

Heating of pressurized containers can result in an explosion

The best and most common example of Gay-Lussac’s law can be observed in a pressure cooker. When the cooker is heated, the pressure inside it increases and this high pressure and temperature cooks food faster. The picture below illustrates the process when there is an increase in the absolute temperature of the gas at constant mass and volume. 

Real-life examples of Gay Lussac’s law

Things to Remember

• Gay Lussac’s law states that pressure exerted by any gas with a given mass and at a constant volume directly varies with absolute gas temperature.
• Gay Lussac’s law can be mathematically represented as P α T.
• According to Gay Lussac’s Law, the ratio of initial pressure and temperature is equal to the final pressure and temperature of a gas at constant mass and volume.
• The formula of Gay Lussac’s Law is (P₁/T₁) = (P₂/T₂)
• The best and most common example of Gay-Lussac’s law can be observed in a pressure cooker. When the cooker is heated, the pressure inside it increases and this high pressure and temperature cooks food faster.

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Sample Questions

Ques. The pressure exerted by a gas on the cylinder is 1.5 atm when heated to a temperature of 250k. What could be the initial temperature of gas if the initial pressure is 1 atm. (2 marks)

Ans. Here,

P₁= Initial Pressure = 1 atm

P₂= Final Pressure = 1.5 atm

T₂= final temperature= 250k

T₁= initial temperature = ?

By Gay-Lussac’s Law,

P₁T₂ = P₂T₁

1 x 250 = 1.5 xT1

T₁ = 166.66k

Ques. The pressure of a gas of deodorant can is 3 atm at a temperature of 300k. What is the final pressure of the gas when heated to 900k?  (2 marks)

Ans. Here,

P₁= Initial Pressure = 3 atm

P₂= Final Pressure =?

T₂= final temperature= 900 k

T₁= initial temperature = 300 k

By Gay-Lussac’s Law,

P₁T₂ = P₂T₁

3 * 900 = P2 * 300

P₂= 9 atm

Ques. The pressure of a gas doubles when the temperature increases from 300k. Find the final temperature.  (2 marks)

Ans. Here,

P₁= Initial Pressure = P atm

P₂= Final Pressure = 2P atm

T₂= final temperature= ?

T₁= initial temperature = 300 k

By Gay-Lussac’s Law,

P₁T₂ = P₂T₁

P * T₂ = 2P * 300k

T₂ = 600k

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Ques. If the pressure of gas increases to 5 atm after the temperature is increased from 100 k to 150 k. Find the initial pressure of the gas.  (2 marks)

Ans. Here,

P₁= Initial Pressure = ?

P₂= Final Pressure = 5 atm

T₂= final temperature= 150 k

T₁= initial temperature = 100 k

By Gay-Lussac’s Law,

P₁T₂ = P₂T₁

P₁ * 150 = 5 * 100k

P₁= 3.33 atm

Ques. If the temperature of a gas is made half at constant volume, what would be a relationship between initial and final pressure.  (2 marks)

Ans. Here,

Let, T₁= initial temperature = T

P₁= Initial Pressure = P

Then, T₂ = final temperature= T/2

P₂= Final Pressure = ?

By Gay-Lussac’s Law,

P₁T₂ = P₂T₁

P * T/2 = P₂ * T

P₂ = P/2

Therefore, the final temperature is also to be halved.

Ques. In a fire extinguisher, if the exploding pressure is 10 atm and it is kept at 2 atm initially. If the temperature is increased from 300 k to 600 k, will it explode or not?  (2 marks)

Ans. Here,

P₁= Initial Pressure = 2 atm

P₂= Final Pressure =?

T₂= final temperature= 600 k

T₁= initial temperature = 300 k

By Gay-Lussac’s Law,

P₁T₂ = P₂T₁

2 * 600 = P2 * 300k

P₂ = 4 atm

Hence, the final temperature is less than than 10 atm. So, it will not explode.

Read More: Partial Pressure

Ques. State the formula for Gay Lussac’s Law?  (2 marks)

Ans. Gay Lussac’s Law is somewhat similar to the ideal gas law as the volume of the gas is kept constant in both. At constant volume, the pressure of a gas is directly proportional to temperature in Gay Lussac’s law. Therefore,

P/T = constant

The standard formula for Gay Lussac’s Law is given by:

P₁ * T₂ = T₁* P₂

Ques. What is Charles Law?  (2 marks)

Ans. Charles law states that “Gas’s volume is equal to a fixed value as determined by Kelvin’s scale and compounded by its temperature”.

Ques. Mention some importance of Gay Lussac’s Law.  (2 marks)

Ans. Gay Lussac’s law makes people aware of the fact that increasing the temperature increases the pressure and vice versa. This factual information is what helps us to determine the warning on fire reducer that it should not be placed in a hot place, used to increase pressure in a petrol engine to initiate combustion, etc. It is used in many practical implementations.

Ques. Is Avogadro’s Law applicable to our daily life?  (2 marks)

Ans. Yes, Avogadro’s Law mainly states that the amount of gas is directly proportional to the number of moles of gas. Hence, we are pushing more gas molecules in football or a tyre of a vehicle to increase its volume. And if more moles are pushed, due to excessive volume, tyres blast.

Ques. Mention some applications of Avogadro’s law.  (2 marks)

Ans. Avogadro’s law is used in daily life to determine the relationship between relative molecular mass and relative vapour density of the gas. It is also used to determine the atomicity of gases.

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