# Charles’s law calculator

`{"calculator":"charles-s-law"}`

## How to use our Charles’s law calculator?

Our Charles’s law calculator helps to calculate the values of the Charles’s law. This law has 4 different values:

• V1 is the initial volume of the gas
• T1 is the initial temperature of the gas
• V2 is the final volume of the gas
• T2 is the final temperature of the gas

When 3 of these values are given in the calculator, it will automatically calculate and display the empty value.

The volume is by default expressed in m³ and the temperature in °K. These units can be changed by clicking on it and selecting another unit.

## Charles’s law

The Charles’s law is one of the laws of the thermodynamics constituting the law of ideal gases. The Charles’s law links the volume and the temperature of an ideal gas at a constant pressure.

The law was named after the French physicist and chemist Jacques Charles (1746 – 1823). The law was published for the first time by Louis Joseph Gay-Lussac (1778 – 1850), but it was discovered by Jacques Charles in 1787.

## Definition

The Charles’s law describes the relation between the volume and the temperature of a gas. This law specifies that at constant pressure, the volume of a certain quantity of an ideal gas is proportional to its temperature.

## Explanation

This definition means that when the pressure is kept constant, an increase in the temperature of a gas leads to an increase of its volume. On the other hands, when the temperature of the gas decreases, the volume of the gas decreases.

The graphic of the volume in function of the temperature (at constant pressure) is typical of a directly proportional relation. The mathematical expression of this type of curve is:

V ∝ T or V/T = constant or V = kT

There is no need to know the exact value of the constant to apply the law between two volumes of a gas under different temperature at the same pressure. Indeed, the Charles’s law formula allows to compare two situations of the same gas when the quantity of gas and the pressure are constant.

## Charles’s law formula

The definition of the Charles’s law gives the following formula:

V1 / T1 = V2 / T2

Where:

• V1 is the initial volume of the gas in m³
• T1 is the initial temperature of the gas in °K
• V2 is the final volume of the gas in m³
• T2 is the final temperature of the gas in °K

## Charles’s law and the absolute zero

The Charles’s law seems to define that the volume of a gas will be 0 at the absolute zero temperature, define as the 0°K (-273.15 °C). But this is not physically correct because gases turn into liquids at a low temperature.

## Limitations of the Charles’s law

The law is not available at high pressure and low temperature.

## Daily Life application of the Charles’s law

Daily life has numerous applications of the Charles’s law. One of the best examples is the hot air balloon. Indeed, the air balloon is made of an envelope that stores the air. When the air is heated in the envelope the temperature increases. So following the Charles’s law the volume also increases. Therefore, the density of the air in the envelope decreases to become lighter than the density of the surrounding atmosphere. As a result, the balloon gains altitude.

On the opposite, the decrease of the temperature in the balloon brings a decrease in the volume of the gas. Therefore, the density of the air inside the envelope decreases to become heavier than the surrounding atmosphere. As a result the balloon loses altitude.