Charles' Law: Liquids And Their Compressibility

Charles's Law, also known as the Law of Volumes, is an experimental gas law that describes how gases tend to expand when heated. It was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles. The law states that if pressure remains constant, the volume of a mass of gas is proportional to its absolute temperature. This relationship can be expressed as V ∝ T, where V is the volume of the gas and T is the temperature of the gas measured in Kelvins. Charles's Law applies specifically to gases, and not to liquids or solids, as it deals with the unique behaviour and properties of gases.

Charles's Law and temperature

Charles's Law, also known as the Law of Volumes, is an experimental gas law that describes the relationship between the volume and temperature of a gas. It was formulated by Jacques Charles in 1787 and refined by Joseph Louis Gay-Lussac in 1808.

The law states that if the pressure remains constant, the volume of a gas is directly proportional to its absolute temperature. In mathematical terms, this can be expressed as:

> V ∝ T

Or

> V/T = k

Where V is the volume of the gas, T is the absolute temperature in Kelvin, and k is a constant for a particular pressure and amount of gas. This means that as the temperature of a gas increases, its volume will also increase proportionally, and conversely, a decrease in temperature will lead to a decrease in volume.

Charles's Law is derived from the basic principles that gases tend to expand when heated and contract when cooled, while the pressure and amount of gas remain constant. This behaviour is unique to gases and is not observed in solids or liquids due to the presence of intermolecular attractions in these states of matter.

The law can be applied to understand various phenomena, such as the expansion of a gas in a closed container when heated or the change in volume of a gas when it is cooled. It also has practical applications, such as in the design of pressure relief valves on gas cylinders, where an increase in temperature and pressure inside the cylinder can lead to an explosion if not properly regulated.

Charles's Law is one of several gas laws that describe the behaviour of gases, along with Boyle's Law, Avogadro's Law, and Amontons' Law. These laws provide valuable insights into the relationship between pressure, volume, and temperature in gases and have various practical applications in fields such as engineering, chemistry, and clinical settings.

Charles's Law and gases

Charles's Law, also known as the Law of Volumes, is an experimental gas law that describes how gases tend to expand when heated. It was named after scientist Jacques Charles, who formulated the original law in his unpublished work in the 1780s. However, it was French physicist Joseph-Louis Gay-Lussac who presented the discovery to the French National Institute in 1802, crediting it to Charles.

Charles's Law states that the volume of a given mass of gas varies directly with the absolute temperature of the gas when pressure is kept constant. The absolute temperature is the temperature measured with the Kelvin scale, as zero on this scale corresponds to a complete stoppage of molecular motion. The law can be expressed mathematically as:

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

Where:

• V is the volume of the gas
• T is the temperature of the gas (measured in kelvins)
• K is a constant for a particular pressure and amount of gas

This law describes how a gas expands as the temperature increases, and conversely, how a decrease in temperature will lead to a decrease in volume. This relationship can be observed in the equation:

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

Where:

• V1 is the initial volume of the gas
• T1 is the initial temperature of the gas (in kelvins)
• V2 is the final volume of the gas
• T2 is the final temperature of the gas (in kelvins)

By keeping the pressure constant, Charles's Law demonstrates that the volume of a gas is directly proportional to its absolute temperature. This means that as the absolute temperature increases, the volume of the gas will also increase proportionally.

It is important to note that Charles's Law is a special case of the general gas law and is derived from the kinetic theory of gases. The kinetic theory relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules that make up the gas, including their mass and speed.

Charles's Law and liquids

Charles's Law, also known as the Law of Volumes, is an experimental gas law that describes how gases tend to expand when heated. It was discovered by Jacques Charles in 1787 and refined by Joseph Louis Gay-Lussac in 1808. The law states that when the pressure on a sample of dry gas is held constant, the volume of the gas is directly proportional to its absolute temperature. This relationship can be expressed mathematically as:

> {\displaystyle V\propto T}

> {\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}

Where V is the volume of the gas, T is the temperature of the gas (measured in kelvins), and k is a constant for a particular pressure and amount of gas.

Charles's Law applies specifically to gases and not to liquids or solids. This is because gases have distinct properties that differ from those of solids and liquids. Gases do not have a fixed volume or shape, whereas solids and liquids do due to the intermolecular attraction between their particles. Additionally, the particles in a gas are in constant, random motion, and they collide elastically with each other. These characteristics of gases are what make them amenable to the principles outlined in Charles's Law.

However, it is worth noting that Charles's Law can be applied to the vapours of volatile liquids if the temperature is well above the boiling point. This qualification highlights the unique behaviour of gases at higher temperatures, which aligns with the principles outlined in Charles's Law.

In summary, Charles's Law describes the relationship between the volume and temperature of a gas, specifically stating that as the temperature of a gas increases, its volume will also increase proportionally, provided that the pressure remains constant. This law is applicable to gases due to their distinct characteristics, such as variable volume and shape, random motion, and elastic collisions between particles. While Charles's Law does not directly apply to liquids, it can be relevant to the vapours of volatile liquids under certain temperature conditions.

Charles's Law and solids

Charles's Law, also known as the law of volumes, is a law that applies to gases. It describes how gases tend to expand when heated and contract when cooled. This experimental law was formulated by Jacques Alexandre César Charles, a French scientist, in the 1780s, although it was not published at the time.

The law states that when the pressure on a sample of dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion. This relationship can be expressed as:

${\displaystyle V\propto T}$

${\displaystyle {\frac {V}{T}}=k,\quad {\text{or}}\quad V=kT}$

Here, V is the volume of the gas, T is the temperature of the gas in Kelvin, and k is a constant for a particular pressure and amount of gas.

This law does not apply to solids or liquids because they have a fixed volume. This is in contrast to gases, which have no fixed volume and will expand to fill the volume of their container.

While Charles's Law does not directly apply to solids, the principles behind it can be observed in solids to some extent. For example, the kinetic theory of gases relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules that make up the gas, such as mass and speed. Similar principles can be applied to solids, where the volume can be related to the kinetic energy and motion of molecules. However, unlike gases, solids do not readily change volume in response to changes in temperature or pressure due to the fixed arrangement of their particles.

Charles's Law and pressure

Charles's Law, also known as the law of volumes, is an experimental gas law that describes how gases tend to expand when heated. It was first formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles.

Charles's Law states that if pressure remains constant, the volume of a mass of gas is proportional to its absolute temperature. The absolute temperature is always 273 Kelvin more than the centigrade temperature. This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume.

The relationship of direct proportion can be written as:

V ∝ T

Or

V = kT

Where:

• V is the volume of the gas
• T is the temperature of the gas (measured in Kelvins)
• K is a constant for a particular pressure and amount of gas

The law can also be used to compare changing conditions for a gas. We can use V1 and T1 to stand for the initial volume and temperature of a gas, and V2 and T2 to stand for the final volume and temperature. The mathematical relationship of Charles's Law then becomes:

V1/T1 = V2/T2

This equation can be used to calculate any one of the four quantities if the other three are known. The direct relationship will only hold if the temperatures are expressed in Kelvin.

For example, if a balloon is filled to a volume of 2.20 L at a temperature of 22°C, and the balloon is then heated to a temperature of 71°C, we can use Charles's Law to find the new volume of the balloon. We first rearrange the equation to solve for V2:

V2 = V1 * T2/T1

Then, we substitute the known quantities into the equation and solve:

V2 = 2.20 L * 344 K/295 K = 2.57 L

Charles's Law, along with Boyle's Law, Avogadro's Law, and Gay-Lussac's Law, forms the basis for the Combined Gas Law, which allows for the derivation of any of the relationships needed by combining all the changeable pieces in the ideal gas law.

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