# Charles's Law

This is part of Year 11 HSC Chemistry course under the topic of Gas Laws.

### HSC Chemistry Syllabus

• Conduct investigations and solve problems to determine the relationship between the Ideal Gas Law and:
• Charles's Law

### Gas Laws

Charles's law is one of the four individual gas laws which were combined to describe the ideal gas law.

The gas laws describe the behaviour of gases under ideal circumstances and assume their properties that ideal gases:

• Have a low density since the spaces between the particles of gas are large
• Are free flowing/forming meaning that they fill the volumes of their containers and can leak through cracks
• Are compressible and expandable
• Are diffusive meaning that they travel from areas of higher concentration to areas of lower concentration.

Charles's law focuses on the directly proportional relationship between temperature and volume when pressure and amount of gas are kept constant.

### Charles's Law

Charles's Law is named after Jacques Charles, an 18th-century chemist who helped influence the development of the hot air balloon .

Charle's law states that the volume that is occupied by a gas is directly proportional to its temperature when the pressure and amount of gas are kept constant. Mathematically the relationship described by Charles's Law can be expressed as

$$V \propto T$$

and thus

$$\frac{V_1}{T_1} = \frac{V_2}{V_2}$$

Where:

• V_1 and T_1 represent the initial volume and temperature
• V_2 and T_2 represent the volume and temperature after a change has been imparted on the gas system.

In the context of Charles's Law, temperature refers to the average kinetic energy which is exhibited by particles of gas while volume refers to the space that is occupied by those gas particles.

Units of Measurement:

• Pressure:
• Pascal (Pa)
• 1 Kilopascal (kPa) = 1000 Pa
• 1 Atmosphere (atm) = 101325 Pa.

• Volume
• Milliliter (mL)
• 1 Liter (L) = 1000 mL

### Deriving and understanding Boyle's Law

The ideal gas law is given by the formula:

$$PV = nRT$$

Where:

• P is pressure (in kPa)
• V is volume (in L)
• n is the number of moles of gas
• R is the universal gas constant = 8.314 J mol–1 K–1
• T is temperature (in Kelvin)

The equation can be rearranged into

$$V = \frac{nRT}{P}$$

When pressure and amount are held constant, the expression \frac{nR}{P} is equivalent to a constant k. Thus the following mathematical equation can also be obtained:

$$V = kT$$

For this relationship to be true, an increase in volume must lead to an equivalent increase in temperature by a factor of 'k' and a decrease in volume must lead to an equivalent increase in temperature. Thus when pressure and amount are held constant, according to the ideal gas law

$$V \propto \frac{1}{T}$$

The relationship described by Charles's Law is demonstrated in the graph below. Note that when the temperature is 0 Kelvin, the volume is a non-zero amount. This means an ideal gas still occupies a certain volume when the kinetic energy of gas molecules is zero at 0 K.

Real-World Examples & Practical Applications

Understanding Charles's law is crucial not just in academic settings but also for everyday applications including hot air balloon and break baking functions.

1. Hot air balloonWhen a flame is introduced under the balloon on the top section of the wicker basket, the air in the space underneath the balloon starts to expand and rises to fill the hot air balloon. Because the air continues to expand, the density of the air inside of the balloon is decreased and rises, allowing the generation of lift that is necessary for the basket to lift off.

2. Bread baking: When the dough is first kneaded, small particles of gas are trapped within its structure. However, when the bread is baked, these molecules begin to vibrate with increased kinetic energy and the space that they occupy increases. The pressure of these pockets of air are unable to escape through the bread dough and continue to expand.These holes which are caused from the expansion of gas can be seen in the cross section of a slide of bread