# Charles Law Formula

## Charles Law Formula

As one of the gas laws, Charles’ law describes the relationship between the volume and temperature of a gas. The volume of a fixed amount of dry gas is directly proportional to its absolute temperature when pressure is held constant. If two measurements are directly proportional, any change made to one will directly affect the other. The Extramarks website offers students a better understanding of the Charles Law Formula. Jacques Charles, a French scientist, discovered in 1787 that when a gas’s temperature changes, its volume changes as well. The concept became Charles’ law when Joseph Gay-Lussac modified it and generalised it in 1802. Charles Law Formula holds true when a gas has a very high temperature and a low pressure. In solving problems related to Charles Law Formula, Kelvin is preferred over Celsius. Temperature is measured in Kelvins (T), also known as Absolute Temperature. Temperatures in centigrade/Celsius are converted to Kelvin scale by adding 273 to them.

## What is Charles Law?

There are many applications of Charles Law Formula in the daily lives of people.

• Helium balloons and balls shrink in cold weather or environments.
• It is common for inner tubes to swell in bright sunlight.
• The capacity of the human lungs will also decrease in colder weather. On a freezing winter day, jogging or participating in sports becomes difficult.
• Charles Law Formula can be applied to our daily lives in the form of a hot air balloon that floats in the air. As the air inside the balloon is heated by the torch, the particles move faster and disperse, allowing the balloon to float since the air inside is less dense than the surrounding air.
• The kitchen is no exception to Charles Law Formula. Those who have tried their hand at baking are probably familiar with the substance most commonly used in cooking, namely yeast. To make bakery products fluffy, yeast is often used in baking. Bubbles of carbon dioxide are released by yeast. A high temperature causes these carbon dioxide bubbles to expand even more. Increased temperature causes the carbon dioxide bubbles to expand, causing the bakery products to become fluffy.

In the field of gas dynamics, Charles Law Formula is regarded as an experimental law. The expansion of gases when heated is explained by this law. According to Charles Law Formula, a gas’ quantity is affected by the temperature at constant pressure. In this law, the gas expands when the temperature increases; conversely, a decrease in temperature will cause the volume to decrease. The purpose of this article is to discuss the Charles law Formula and its properties. V=kT is the equation of the law.

• K may be a constant.
• T = Temperature of the gas
• V= Volume of the gas

A consequence of the Charles Law Formula is that the quantity of gas will drop to zero at certain temperatures (266.66 °C, according to Gay-Lussac’s numbers and 273.15 °C, according to Charles Law Formula).  Due to its zero energy, gas molecules are restricted from moving at room temperature. From his experiments, Charles concluded that at constant pressure, the quantity of the amount of a gas decreases or increases by 1⁄273 (now 1⁄273.15) multiplied by the quantity at 0 °C for each 1 °C fall or rise in the temperature. It was named after Jacques Charles, who formulated the original law in an unpublished work from the 1780s. Between 2 and 30 October 1801, John Dalton presented two essays in which he demonstrated by experiment that all gases and vapours expanded the same amount between two fixed points of temperature. French natural philosopher Joseph Louis Gay-Lussac confirmed the discovery in a presentation to the French National Institute in 1802, although he credited Jacques Charles’ unpublished work from the 1780s. A century earlier, Guillaume Amontons and Francis Hauksbee had described the basic principles. First demonstrated by Dalton, the law applied generally to gases, as well as to vapours of volatile liquids at high temperatures. Gay-Lussac agreed. Gay-Lussac failed to prove that the equation relating volume to temperature was linear based on measurements taken at the two thermometric fixed points of water.

### Solved Examples

Question 1:

A gas occupies a volume of 400cm3  at 0 °C and 780 mm Hg. What volume (in litres) will it occupy at 80 °C and 780 mm Hg?

Solution: Given,

V1= 400 cm³

V2 =?

T1= 0 °C= 0+273 = 273 K

T2= 80 °C= 80+273 = 353 K

Using Charles Law,

V1/V2 = T1/T2

V2 = 517.21 cubic cm = 0.517 litre

Question 2:

If the final volume of a gas at 100 K is 6 L, find its initial volume at 150 K

Solution:

Given,

V1=?

V2 =6 L

T1= 150 K

T2= 100 K

Using Charles Law,

(V1)(T1)=(V2)(T2)

V1 = 9 L