# Charles' Law

## What is Charles' law?

Charles' law had been predicted earlier, in 1702, in the work of Guillaume Amontons. However, the law was first formally published in 1802 by Gay-Lussac, but it referred to the unpublished work of Jacques Charles in 1787, so it is attributed to Charles.

On the other hand, Gay-Lussac related pressure and temperature as directly proportional quantities in the so-called second Gay-Lussac law.

Charles' law can be stated as follows:

At constant pressure, the volume of a mass of gas is directly proportional to its absolute temperature (in degrees Kelvin).

V1 /T1 = V2/T2

## Charles' experiment

It answers the question what happens to the volume and temperature of an ideal gas when we keep the pressure constant?

In 1787, Jack Charles first studied the relationship between the volume and temperature of a gas sample at constant pressure and observed that when the temperature was increased the volume of the gas also increased and that on cooling the volume decreased.

Charles observed that volume and temperature are directly proportional quantities; the quotient V/T remains constant for the same pressure.

V/T = cte

V1/T1 = V2/T2

Thus, increasing the temperature also increases the average speed of the molecules and their average distance, thus increasing the volume:

fig-1

## Solved exercises on Charles' law

### 1) A hot air balloon occupies a volume of 100 m3 at a temperature of 30 ºC. What volume will the same air occupy if it is heated to a temperature of 150 ºC?

Solution:

V1 = 100 m3;  T1 = 30 ºC; T2 = 150 ºC

In this equation, temperatures are always used in absolute degrees (Kelvin = ºC + 273), therefore:

V1 = 100 m3;  T1 = 303 K; T2 = 423 K

V1/T1 = V2/T2

V2 = (T2·V1)/T1

V2 = (423 K · 100 m3) / (303 K)

V2 = 140 m3

### 2) The volume of a nitrogen sample is 3 liters at 75°C. What volume will the gas occupy at 40°C, if the pressure remains constant.

Solution:

V1 = 3 L;  T1 = 75 ºC; T2 = 40 ºC

Para esta ecuación, las temperaturas siempre se utilizan en grados absolutos (Kelvin = ºC + 273), por tanto:

V1 = 3 L;  T1 = 348 K; T2 = 313 K

V1/T1 = V2/T2

V2 = (T2·V1)/T1

V2 = (313 K · 3 L) / (348 K)

V2 = 2.7 L

Por lo que podemos observar que el volumen final será de 2.7 litros, esto afirma nuevamente que mientras la temperatura disminuya, el volumen disminuirá.

## Limitations on Charles' law

Gases that perfectly comply with Boyle's and Charles and Gay Lussac's laws are called ideal gases.

In principle, such gases do not exist. However, the ideal gas model is a valid approximation for the description of real gases in two situations:

• When at high temperatures
• When at low pressures

Real gases, at pressures and temperatures close to ambient (1 atm and 25ºC), act as ideals.

For these conditions we can relate the pressure, volume and temperature of a gas quantity by means of the equation of state of ideal gases pV=nRT

This hypothesis is very useful to study the behavior when they are far from a change of state, but fails when the gas is close to liquefaction or sublimation.

In these cases, the interactions between the gas molecules are no longer negligible, nor is the volume they occupy.

Back to the gas laws page.