# Gay Lussac’s Law

Gay Lussac’s is one of the Ideal gas laws that relates the pressure of the gas with its absolute temperature when its volume is kept constant. The basic statement of Gay Lussac’s Law is, the pressure produced by a gas is directly proportional to its temperature if mass and volume are kept fixed. Gay Lussac’s Law has wide application in sciences and also in our everyday life. Gay Lussac’s Law as the name suggests was given by the French chemist Joseph Gay-Lussac in the year 1808.

In this article, we’ll learn about Gay Lussac’s Law, its formula, derivation, and others in detail.

## What is Gay-Lussac’s Law?

Gay-Lussac’s law states that the pressure exerted by a gas varies directly with the absolute temperature of the gas if the mass of the gas is fixed and the volume is constant. i.e. The pressure exerted by a gas is proportional to the temperature of the gas at constant volume.

P ∝ T

Adding proportionality constant k,

P = kT

Now, at temperature T_{1} and pressure P_{1}

P_{1} = kT_{1}…(1)

Also, at temperature T_{2} and pressure P_{2}

P_{2 }= kT_{2}…(2)

Now, combining eq(1) and eq(2)

P_{1}/ T_{1}= P_{2 }/ T_{2}

Pis the pressure exerted by the gasTis the absolute temperature of the gas

## Gay Lussac’s Law Graph

Gay Lussac’s law is expressed by the equation,

**P = kT…(1)**

Mathematically this equation is comparable to y = mx…(2)

Comparing eq (1) with eq (2) we get

y = P, m = k and x = T. Now the graph of the given equation is,

**Formula and Derivation**

The formula for Gay-Lussac’s Law is,

P_{1}/T_{1}= P_{2}/T_{2}where,

Pis the initial pressure,_{1}Tis the initial temperature,_{1}Pis the final pressure,_{2}Tis the final temperature_{2}

### Derivation of Gay Lussac’s Law

It is known that the pressure of a gas is proportional to its temperature. This relation can be written as,

P ∝ T

Replacing the proportionality sign with constant k we get,

P = kt

The above equation is valid for all values of pressure and temperature.

Suppose a gas is exerting pressure P_{1} at a temperature T_{1}. The equation that defines this situation is,

P_{1} = kT_{1}

k = P_{1}/T_{1}……… (1)

The temperature of the gas changes to T_{2}, which changes the pressure to P_{2}. This can be expressed as,

P_{2} = kT_{2}

k = P_{2}/T_{2}……… (2)

From (1) and (2) we get,

P_{1}/T_{1}= P_{2}/T_{2}

This derives the Gay Lussac law for gases.

## Gay Lussac’s Law of Gaseous Volumes

Joseph Louis Gay-Lussac in 1808 also proposed the law of Gaseous Volumes which is different from the law of definite proportions. According to Gay Lussac’s Law of Gaseous Volumes, if measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers. Gay Lussac’s Law of Gaseous Volumes works with respect to volume while the law of definite proportion works with the mass of the gas.

**Examples of Gay Lussac’s Law**

Gay Lussac’s Law has a variety of applications some of the examples of Gay Lussac’s law that we observed in our daily life are,

- Increasing the heat to a pressure cooker increases the pressure inside it. This results in less cooking time as the steam does not lose the taste of food to the air due to the sealed container.
- If too much air is put in vehicle tyres, they may over-pressurize due to high temperature. But on a cold day, their pressure reduces which results in underinflation.
- Aerosol cans shouldn’t be kept in high temperatures because heat raises the pressure inside them which may lead to an explosion.

**Read, More**

**Solved Examples on Gay Lussac’s Law**

**Example 1: The initial pressure of a gas inside a tank is 2 Pa at 100 K. Find the final pressure if the gas is heated to a temperature of 200K.**

**Solution:**

We have,

Initial Pressure P

_{1}= 2 Pa

Final Pressure P_{2}= ?

Initial Temperature T_{1}= 100 K

Finial Temperature T_{2}= 200 KUsing the formula we get,

P

_{1}/T_{1}= P_{2}/T_{2}2/100 = P

_{2}/200P

_{2}= 200/50P

_{2}= 4 Pa

Final pressure of the gas P_{2}= 4 Pa

**Example 2: The final pressure of a gas inside a tank is 12 Pa at 200 K. Find the initial pressure if the initial temperature of the gas was 50 K.**

**Solution:**

We have,

Initial Pressure P

_{1}= ?

Final Pressure P_{2}= 12 Pa

Initial Temperature T_{1}= 50 K

Finial Temperature T_{2}= 200 KUsing the formula we get,

P

_{1}/T_{1}= P_{2}/T_{2}P

_{1}/50 = 12/200P

_{1}/50 = 3/50P

_{1}= 3 Pa

Initial Pressure of the gas P_{1}= 3 Pa

**Example 3: The initial pressure of a gas inside a tank is 2 Pa at 300 K. Find the final temperature of gas which increased its pressure value to 8 Pa.**

**Solution:**

We have,

Initial Pressure P

_{1}= 2 Pa

Final Pressure P_{2}= 8 Pa

Initial Temperature T_{1}= 300 K

Finial Temperature T_{2}= ?Using the formula we get,

P

_{1}/T_{1}= P_{2}/T_{2}2/300 = 8/T

_{2}T

_{2}/8 = 300/2T

_{2}/8 = 150T

_{2}= 1200 K

Finial Temperature of the gas T_{2}= 1200 K

**Example 4: The final pressure of a gas inside a tank is 15 Pa at 900 K. Find the initial temperature if the initial pressure of gas was 3 Pa.**

**Solution:**

We have,

Initial Pressure P

_{1}= 15 Pa

Final Pressure P_{2}= 3 Pa

Initial Temperature T_{1}= ?

Finial Temperature T_{2}= 900 KUsing the formula we get,

P

_{1}/T_{1}= P_{2}/T_{2}3/T

_{1}= 15/900T

_{1}/3 = 900/15T

_{1}/3 = 60T

_{1}= 180 K

Initial Temperature of the gas T_{1}= 180 K

## FAQs on Gay-Lussac’s Law

### Q1: What is Gay Lussac’s law formula?

**Answer:**

Gay Lussac’s law is an Ideal gas law that deals with the ideal gas at constant volume. According to this law, at constant volume, the pressure of the gas is directly proportional to the temperature of the gas. Gay Lussac’s law formula is

,

P / T = constant

### Q2: What does Charles law state?

**Answer:**

According to Charles law, “At constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature.”

### Q3: Why is Gay Lussac’s law important?

**Answer:**

Gay Lussac’s law is important because, with its help, we can find the temperature of the gas if the pressure variation of the gas is given at constant volume.

### Q4: What are the types of Ideal Gas Laws?

**Answer:**

There are four different types of Ideal Gas Laws, which are

- Boyle’s Law
- Charles’s Law
- Avogadro’s Law
- Gay Lussac’s Law

### Q5: What is Avogadro’s law?

**Answer:**

According to Avogadro, “The number of molecules of different gases at similar conditions of temperature, pressure, and volume is always the same.”

### Q6: What is the difference between Gay Lussac’s Law and Charles’s Law?

**Answer:**

The main difference between Gay Lussac’s Law and Charles’s Law is,

According to Charles law, the volume of a gas is directly proportional to its absolute temperature at constant pressure, whereas according to Gay Lussac’s Law for a fixed volume of gas, the pressure is directly proportional to its temperature.

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