## Charles Law in General Gas Equation

As the temperature and pressure of an ideal gas remain constant, Charles' law states that the volume is directly proportional to its absolute temperature at constant pressure. According to the law, when constant pressure is applied to a sample of dry gas, the Kelvin temperature, and the volume will be directly proportional.

A French physicist named Jacques Charles first proposed this law in the year 1780. His unpublished work provides extensive details about this law.

### What is Charles Law?

A detailed explanation of how gas expands when the temperature rises is provided by Charles' Law, also known as the law of volumes. When the temperature decreases, the volume will decrease, and vice versa.

According to the above statement, we can write the following when comparing a substance in two different circumstances:

\[\frac {V_2} {V_1}\] = \[\frac {T_2} {T_1}\]

OR,

\[\frac {V_1} {T_2}\] = \[\frac {V_2} {T_1}\]

According to the above equation, the volume of the gas increases proportionately as absolute temperature increases.

Charles law can therefore be stated as a special case of the ideal gas law. A constant pressure law applies to ideal gases, where the temperature and volume keep changing, but the pressure remains constant.

### General Gas Equation - Charles Law

In a popular laboratory experiment, a fully inflated balloon is placed inside a container with liquid nitrogen (which is at a temperature of -196 ˚C), and we can observe that the balloon shrinks to about 1/1000th of its former size. Similarly, if we keep an inflated balloon in the fridge it too shrinks considerably. After this, if the balloon is carefully removed from the container or the fridge is allowed to slowly warm itself to room temperature, it will regain the size that it was as before; it was shrunk down due to the cooling of liquid nitrogen. This is one of the simplest experiments which can be performed to demonstrate the effects of temperature on gases.

The law that is used to explain the effects of temperature on gases under constant pressure is called as Charles Law. When a gas is heated, the molecules gain more energy and move about, thus expanding the space that they need to occupy. It is named in recognition of the French scientist and balloon flight pioneer Jacques Alexandre César Charles. The statement of Charles law is "The volume of any gas is directly proportional to its temperature on the Kelvin scale under the same amount of pressure”.

According to Charles law, the directly proportional relationship between temperature and volume is as follows

V ∝ T

Or

\[\frac {V} {T} = k\]

Where,

V is the volume of the given gas

T is the temperature of the given gas measured in kelvins

k is a constant, obtained by dividing V by T

For every 1 °C drop in the temperature of a liquid, the volume of a fixed mass of gas decreases, while the volume of that gas increases by 1/273.

Therefore,

VT = V0 + (1/273 × V0) × T

VT = V0 + (1 + T/273)

Where:

VT is the volume of the given gas at the temperature T

V0 is the volume of the given gas at 0 °C

### The discovery and naming of the law

Jacques Alexandre César Charles was a French mathematician, scientist, inventor, and balloonist who established the law in his honor. One of his most enduring achievements was launching a hydrogen-filled gas balloon manned by a human. Natural philosopher Joseph Louis Gay-Lussac in 1802 published a paper showing how gases expand when heated, within days after the first manned launch of the hot air balloon. In the 1780s, Jacques Charles wrote about it in unpublished work. Charles Law was also named by Gay-Lussac in his honor.

In 1787, Charles filled the same volume of five containers with various gases. Once the containers reached 80 degrees, he raised the temperature. As a result, all the gases increased by about the same amount. In 1802 Gay-Lussac published a paper referring to this experiment. As a result, Charles observed that the volume of a gas increases linearly with the absolute temperature of the gas under constant pressure

The formula created by Charles was \[\frac {V_1} {T_1}\] = \[\frac {V_2} {T_2}\]

We can also further consider this to give \[\frac {V_1} {T_1}\] = \[\frac {V_2} {T_2}\] = \[\frac {V_3} {T_3}\] = \[\frac {V_4} {T_4}\]

### General Gas Equation based on Charles Law

The General Gas Equation is the product of the combined gas laws for pressure, temperature, and volume. Charles's Law and Boyle's Law are combined to form the General Gas Equation. Boyle's Law describes the relationship between volume and pressure at constant pressure. Gay-Lussac's law states that pressure and temperature are related under constants. They are three of the fundamental principles that make up the General Gas Equation, along with Charles' law that explains the relationship between temperature and volume.

A gas' volume is equal to its temperature divided by its pressure, according to the combined gas law. The equation becomes

V ∝ T

Or,

\[\frac {PV} {T}\] =k

Where:

V is the volume of the given gas

T is the temperature of the given gas measured in kelvins

P is the pressure which the gives gas is subjected to

k is a constant

### Charles's Law has the following problems

According to Charles's Law, volume directly increases or decreases as volume increases or decreases. Since the volume decreases proportionally with the temperature, it follows that the temperature decreases. According to theory, the gas volume should decrease until it reaches zero as the temperature drops. As a result, it would seem that gas should have no volume at absolute zero (a theoretical temperature where gas has zero energy and therefore can't move). Of course, it is true that Charles and Gay-Lussac didn't have experience with liquid air during the time of their research, as liquid air wasn't invented until 1877 even though Charles believed gases such as hydrogen and oxygen could be liquified.

### Examples for Problems Requiring the Application of Charles’s Laws:

A balloon is filled to a volume of 2.40 L at a temperature of 20 °C. The balloon is then heated to a temperature of 70 °C. Assuming the pressure remains constant throughout, find the new volume of the balloon.

Solution:

Given:

V1 = 2.40 L

T1 = 20 °C = 293 K

T2 = 70 °C = 343 K

V2 =?

We know \[\frac {V_1} {T_1}\] = \[\frac {V_2} {T_2}\]

V2 = V1 × \[\frac {T_2} {T_1}\]

V2 = 2.40 × \[\frac {343} {293}\]

V2 = 2.80 L

A sample of gas has an initial volume of 30.8 L and an initial temperature of −67°C. What must be the temperature of the gas for its volume to be 21.0 L?

Solution:

Given:

V1 = 30.80 L

T1 = -67 °C = 206 K

T2 =?

V2 = 21.0 L

We know \[\frac {V_1} {T_1}\] = \[\frac {V_2} {T_2}\]

T2 = V2× \[\frac {T_1} {V_1}\]

T2 = 30.80 × \[\frac {206} {21.0}\]

T2 = 302 K =29 °C

If V1 = 3.60 L and T1 = 255 K, what is V2 if T2 = 102 K?

Solution:

Given:

V1 = 3.60 L

T1 = 255 K

T2 = 102 K

V2 =?

We know \[\frac {V_1} {T_1}\] = \[\frac {V_2} {T_2}\]

V2 = V1 × \[\frac {T_1} {T_2}\]

V2 = 3.60 × \[\frac {255} {102}\]

V2 = 9 L

Gas laws are defined at idea conditions and are then utilized in real-time situations for making proper calculations. To answer questions related to Charles law, you need to focus on clarifying your doubts.

## FAQs on Charles Law

**1. What is Charle's Law's Application to Real Life?**

There are many applications of this law in daily life. Among them are:

When the balloons are in a cold environment or in cold weather, they shrink.

A person's lung capacity decreases in the winter when it is cold. Taking part in a winter sport on a freezing day is difficult for the athletes, and it makes jogging more difficult for people.

**2. Is there anything that cannot be changed in Charles Law?**

Charles Law maintains constant pressure. As Charles law states, the volume of a gas is proportional to its temperature assuming a constant pressure.

**3. What is the significance of Charles Law?**

Gases tend to expand when heated according to Charles' Law, an experimental gas law. According to the law of thermodynamics, a quantity of gas held at constant pressure will exhibit a direct relationship between its volume and its temperature.

**4. Which two variables are involved in Charles Law?**

Charles' law states that temperature and volume have a direct relationship. Charles's law provides a guide to estimating volume and temperature changes when the parameters of a system change.

**5. Why do ideal gases not have a volume?**

Molecules of ideal gas do not occupy any volume. Due to the molecules expanding into a large region of space, gas molecules take up volume, but these molecules were approximated as point particles that cannot have any volume by themselves.