Ideal Gas Law

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The Ideal gas law describes the behavior of a hypothetical real or ideal gas under various conditions. Emile Clapeyron proposed it in 1834.


Ideal gas law states that “for a given amount of gas, when the volume of the gas is compressed, the temperature of the gas increases. Similarly, when the volume of the gas increases, its temperature decreases”.

Mathematically, the ideal gas law can be implied as

PV = nRT
Where P is pressure,
V is volume,
n is number of moles of the gas ,
R is gas constant ,
T is the absolute temperature .

Discovery of Ideal Gas Law

The ideal gas law is derived from a combination of four important laws of chemistry: Boyle's law, Avogadro's law, Gay-Lussac Law and Charles law.

Boyle's law

Robert Boyle discovered this law. It states that under constant temperature, the pressure exerted by a gas is inversely proportional to the volume of the container it is stored in. Its mathematical representation is as below:

Where P = Pressure,
V = Volume
k = constant

Charles Law

Jacques Charles has derived this. In this law, the pressure is kept constant. Under this condition, the volume of a given gas is directly proportional to its temperature. Its mathematical representation is as below:

Where V = Volume and T = Temperature.

Gay-Lussac's law

Discovered by Gay-Lussac, this law states that the pressure of given gas is directly proportional to its Temperature when the volume of the gas is maintained constant. Its mathematical representation is as below:

Where, P = Pressure and T = Temperature.

Avogadro's law

Amedeo Avogadro derives it. It states that at the same temperature and pressure, equal volumes of all gases, have the same number of molecules. Its mathematical representation is as below:

V = nk
Where V = volume of the gas
n = number of moles of the gas
k = a constant for a given pressure and temperature.

Derivation of Ideal gas law

The ideal gas law equation can be derived from the gas mentioned above laws as follows:

From Boyle’s law, we know :
From Charle’s law, we know: V ~ T
From Avogadro's Law, we know: V ~ n
Combining the above 3 laws, we get:
This can be rearranged as,
R × n × T

PV = nRT where R is the Gas Constant.

Now, do you know how to calculate the values of ideal gas law variables? Well, we would come soon to that before we wind up this discussion.

Applications of Ideal Gas law in real life

Since its inception, the ideal gas law has been finding its uses in many appliances that we come across in our day to day life. Also, many kinds of research and studies have been going on based on this law itself. Some of such applications of ideal gas law are discussed here:

Refrigerator/Air Conditioning

When the coolant gas is made to compress, its temperature increases. Then, this hot gas is made to pass through a radiator which allows the excess heat to escape after which the volume of the gas is allowed to increase by expanding it in the refrigerator. When the gas expands, its temperature goes down, and the heat in the internal section of the refrigerator is drawn out.


Stoichiometry is an important branch of study in chemistry. Ideal gas law is used in stoichiometry in finding the number of moles/volume a given gas can produce when temperature and pressure are kept constant.

Diesel Engine

Ideal gas law is used in determining the efficiency of a diesel engine by keeping the pressure and volume constant. In this case, the temperature and heat are used to calculate the efficiency of energies that are put into and out. These efficiencies are displayed in terms of heat and temperature using the formula PV=nRT, where this gas law helps in preventing the explosions in fuel combustion.

Friends, it may be surprising for you to know that this principle of ideal gas law is behind the following actions as well:

Flying Balloons

A hot air balloon is filled with gas molecules with a certain temperature, at a constant pressure. When pressure and temperature are maintained constant the volume of the gas increases and further adding some more hot air molecules, the balloon will get filled. The density of hot air is lesser that the density of cold air, i, e. the number of molecules in hot air in a given volume is lesser than that of the number of molecules in cold air in the same given volume. Hence, the density of air in hot air balloon will be lesser than that of the density of outside atmosphere because of which the balloon rises into the air and flies.

Have you ever thought that this much science is involved in flying a balloon? Never, isn’t it? We are sure now you know the amazing science behind a flying balloon.

Playing Football

Yes! Though surprising, playing football also depends on this Ideal Gas Law.

The ideal gas law helps us in determining the football volume with respect to the temperature of the outside atmosphere. Suppose when the team wants to play football on a cold day i, e. a day with low temperature, the volume of gas inside the football shrinks. So they have to add some more gas molecules to equalize the volume of football with that of its volume which will be seen on a day with normal temperature. Sounds interesting, what say?

How to use CalculatorHut’s Ideal Gas Law calculator?

A student or a professional in chemistry has to use ideal gas law and its calculations as a part of their daily tasks. As the numerical values of pressure, temperature, R and volume most times contains decimal values or may be in different units, CalculatorHut’s Ideal Gas law calculator becomes very handy for you!

In CalcualtorHut’s ideal gas law calculator, you need to enter the values of known variables in the right hand and left-hand side of the equation. On clicking ‘Calculate’, CalculatorHut’s Ideal gas law calculator gives you instantaneous results. It’s super easy and handy.

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