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Gay-Lussac’s Law Calculator

#### ☛ Derivation

When pressure and volume are varied keeping the temperature as constant, applying Boyle's Law we get:

P1 × V1 = P2 × V ------ (1)

Where P1 and P2 are initial and modified pressures and V and V1 are initial and modified volumes of the given gas.

When pressure is kept constant, and temperature and volume are varied by applying Charles law we get:

T1 × V2=T2 × V ------ (2)

Where T1 and T2 are initial and final temperature and V2 and V are final and initial volumes.

From (1), we get: V = P1 × V1 × P2 ------ (3)

From (2), we get: V = T1 × V2 × T2 ------ (4)

From the right-hand values of (3) and (4): P1 × V1 × T1 = P2 × V2 × T2 = k

That is, P × V=k × T ------ (5)

Finally keeping volume V as constant, from (5) we get: P ~ T, which is the Gay-Lussac’s statement.
#### ☛ Points to note about Gay Lussac’s law

#### ☛ Fun Facts about Gay Lussac’s law

#### ☛ Applications of Gay Lussac’s Law

#### ☛ Why should you use CalculatorHut’s Gay Lussac’s Law calculator?

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The Gay-Lussac’s law was founded by "Joseph Louis Gay-Lussac" in 1802. He was a French man, a chemist and a physicist, and a professor by profession. He derived the law of expansion of gases when heated and was also involved in the upgradation of various tools like barometer and thermometer. His other discoveries were on the reactivity of gases especially in the formation of CO2 and H2O.

Do you know? – As an honor to his contributions, Gay-Lussac’s name was inscribed on the Eiffel Tower, which is one of the 8 wonders of the world.

Statement
**P1 × T1 = P2 × T2**

Where P1 and P2 are the Initial Pressure and Final Pressure respectively measured in the units of atm.

T1 and T2 are the Initial Temperature and the Final temperature, measured in the units of Kelvin.

Gay Lussac’s law defines the relationship between the pressure and temperature of a gas. As per this law, “The pressure of a given gas is proportional to its temperature, at a constant volume.”

This law is mathematically represented as:

Where P1 and P2 are the Initial Pressure and Final Pressure respectively measured in the units of atm.

T1 and T2 are the Initial Temperature and the Final temperature, measured in the units of Kelvin.

We now know that this law states that the pressure of a given gas is directly proportional to its temperature: i, e. P ~ T or PT = k, where k is constant (which is the volume of the gas).

This law can be derived from Charles law and Boyle’s law as below:

Initially P × T = kWhen pressure and volume are varied keeping the temperature as constant, applying Boyle's Law we get:

P1 × V1 = P2 × V ------ (1)

Where P1 and P2 are initial and modified pressures and V and V1 are initial and modified volumes of the given gas.

When pressure is kept constant, and temperature and volume are varied by applying Charles law we get:

T1 × V2=T2 × V ------ (2)

Where T1 and T2 are initial and final temperature and V2 and V are final and initial volumes.

From (1), we get: V = P1 × V1 × P2 ------ (3)

From (2), we get: V = T1 × V2 × T2 ------ (4)

From the right-hand values of (3) and (4): P1 × V1 × T1 = P2 × V2 × T2 = k

That is, P × V=k × T ------ (5)

Finally keeping volume V as constant, from (5) we get: P ~ T, which is the Gay-Lussac’s statement.

The pressure of gases here is measured using a unit called atm. An atmosphere (atm) is a measuring unit for pressure depending on the average atmospheric pressure at the sea level. Altitude and temperature are few of the various conditions on which the actual atmospheric pressure depends on.

Kelvin (denoted with symbol K) is a standard international unit in the measurement of thermodynamic temperature. Kelvin is defined as a fractional value of 1/273.16 of the thermodynamic temperature of the triple point of water temperature, or in other words, the triple point of water temperature is 273.16 K.

Some of the situations in our day to day life where we encounter this law knowingly or unknowingly are:

**Pressure changes in a tire:**You must have noticed that when the temperature of the outside atmosphere increases, the pressure of the gas in the tiers also increases.**The air in a balloon:**Similarly, when a balloon filled with air is kept into a cold room for a while, the pressure inside the balloon also decreases because of the decreases in the temperature of the air inside the balloon.**Heating an aerosol can:**When an aerosol like deodorants or spray paints is heated, the pressure inside those cans increases which is because of the increased temperature. Such a condition can cause the container to explode. This is the reason behind warning being printed on the deodorant bottles or spray cans as ‘Do not put in fire even if the bottle is empty’.

Some of the applications of Gay-Lussac’s law include the following:

**Using a gun to fire:**The Gay Lussac’s law comes to picture when one tries to fire a bullet. When a bullet is fired, a super-heated gas gets generated because of the ignition of the gunpowder. This increases the pressure because of which the bullet moves with high speed and long distance.**Pressure Cooker:**When a pressure cooker containing food is heated, the temperature of the gas or air in it increases causing a rise in the pressure inside the cooker. Note that higher the pressure in the cooker, lower is the time for the food to get cooked.**Cooking in an Oven:**the Same principle holds good for the oven as well. When the oven is heated, the temperature of the air in it increases with a simultaneous rise in pressure. This pressure is what that helps food in the oven to get cooked.

Gay Lussac law is a key criterion for understanding the physics of gases. It is an important concept in many important subjects such as meteorology and organic chemistry. Hence, it is mandatory that one has ample practice about the calculations involved.

CalculatorHut’s free online Gay-Lussac’s calculator lets you calculate the various unknown parameters of Gay-Lussac’s law. You can calculate results easily in any unit of temperature and pressure. If you are preparing for exams or need help for Chemistry assignments, CalculatorHut’s Gay-Lussac calculator would be of immense help. When you are solving problems based on this concept, this online Gay-Lussac’s calculator for free also helps you to verify whether the results that you got are correct or not. With CalculatorHut’s free online chemistry calculators, chemistry is no tougher. Sounds cool, what say?

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