Charles Law: Definition, Equation, Application & Exercise

Charles Law

Charles Law: We would often have ever seen a hot air balloon. The working principle of a hot air balloon is purely superficial and is based on Charles law. The air balloon consists of a bag, a basket to carry passengers, and a fuel source. On igniting the fuel, the air inside the bag heats up. This hot air expands as per Charles's law. So according to Charles's law as the temperature of the air increases, the volume of the air also increases so the same happens in an air balloon. This makes the bag lighter than the atmospheric air surrounding it and the buoyant force pushes the more lightweight envelope up in the air, and it flies.

What is Charles Law?

This Concept of Charles law was named after scientist Jacques Charles, this concept was formulated in the year 1780. Charles law is one of the experimental gas laws that describes how gases tend to expand when it is heated up. According to Charles law is that “ At constant pressure, the Volume of the fixed mass is directly proportional to the temperature ”. Mathematically it can be written as:

V ∝ T

V = kT

Equation and Derivation of Charles Law

As we know at constant pressure, the volume of fixed mass is directly proportional to the temperature. So we can write it as-

V∝T

V = kT 

V/T = k= proportionality Constant

If the temperature is increased to T1 the volume of the gas becomes V1, it can be written as:

V1/T1 = k   ---------------------(1)

And further, the temperature is increased to T2 then the volume of the gas becomes V2

V2/T2 = k   ---------------------- (2)

Equating (1) and (2) we get, 

V1/T1 = V2/T2 

OR, 

V1T2 = V2T1

Where, 

V1 is the Volume of the ideal gas at the T1 temperature

T1 is the temperature of the gas

V2 is the Volume of the ideal gas at the T1 temperature

T2 is the temperature of the gas

k is the proportionality constant

Charles law Graph(Volume-Temperature Relationship)

The Charles law is the volume-temperature relationship, on an increase in the temperature the volume of the gas is expanded. The graph plotted below shown that with an increase in temperature the volume of the gas also increases.

Application of Charles law

Some of the applications of Charles's law are-

Human Lungs: The human lungs are spongy air-filled organs that have an important role in respiration. Air flows into the lungs causing the lungs to expand and flow out when they contract. In winter, as the temperature of the air decreases. As a result, the temperature of the body also decreases. According to Charles's law, which states volume is directly proportional to temperature. Hence, the decrease in temperature also decreases the volume. This causes the lungs to shrink and physical activities like jogging become difficult on freezing winter days.

Pool Float: As a toddler, we all have used a pool float during swimming classes. The Pool floats are filled with air which makes them less dense than water. When water is cooler than air, the air in pool floats shrinks because of a decrease in the temperature of the air inside the floats. This reverse phenomenon happens during hot summer days when the water is much warmer. 

Baking: We can experience the application of Charles's law in our kitchens also. Our delicious bakery products like bread, cakes, and biscuits would not be spongy and soft without yeast. Yeast is a leavening agent that converts sugars in the dough to carbon dioxide gas. When bread and cakes are baked, the conversion accelerates. The gas liberating expands because of increased temperatures in the oven. Ans this expansion causes the bread and cakes to have a spongy appearance.

Exercise based on Charles Law

The solved exercise based on Charles's law is-

Question1: On a ship sailing in the Indian ocean where the temperature is 23.4 °C, a balloon is filled with 2 L air. What will be the volume of the balloon when the ship reaches the Pacific Ocean, where the temperature is 26.1°C?

Solution: According to the question, V1 = 2L

T1 = (23.4 + 273) = 296. 4K

T2 = (26.1 + 273) K = 299.1K

V2 = ?

According to Charles law, V1/T1 = V2/T2  ---------(1)

Subsisting to the value in the above equation, we get,

2/296.4 = V2/ 299.1

V2 = 2L X 299.1K/296.4K

V2 = 2.018 L 

So the volume of the balloon when the ship reaches the Pacific Ocean is 2.018 L 

Question2: Find the initial volume of a gas at 800 K, if the ultimate volume is 4L at 200 K

Solution:  According to the question, T1 = 800K

V2 = 4L

T2 = 200K 

V1 =?

According to Charles law, V1/T1 = V2/T2  ---------(1)

Subsisting to the value in the above equation, we get,

V1 / 8OO = 4 / 200

V1 = 16L 

So the initial volume of the gas is 16L