Charles' Law: Gases Transforming Into 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. The 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. This means that when the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion. However, Charles's Law does not hold true when a gas is brought to extremely cold temperatures, as the gas molecules would eventually condense into a liquid state.

Charles's Law states that the volume of a fixed amount of gas is directly proportional to its temperature when pressure is kept constant

Charles's Law, also known as the law of volumes, describes how gases tend to expand when heated. It was formulated by French physicist Jacques Charles in the late 18th century and states that the volume of a fixed amount of gas is directly proportional to its temperature when pressure is kept constant.

Mathematically, this relationship can be represented by the equation:

> V ∝ T

Where V is the volume of the gas, and T is the temperature of the gas (measured in Kelvins).

This law can also be used to compare changing conditions for a gas. Using initial values of volume (V1) and temperature (T1), and final values of volume (V2) and temperature (T2), the equation becomes:

> V1/T1 = V2/T2

This equation can be used to calculate any one of the four quantities if the other three are known. It's important to note that the temperatures must be expressed in Kelvin for this equation to hold.

Charles's Law is a special case of the ideal gas law and is applicable to ideal gases held at constant pressure, with changing temperature and volume. It is not applicable to gases at low temperatures, as they would eventually condense into a liquid state before reaching absolute zero.

The Kelvin scale must be used to express temperature because zero on the Kelvin scale corresponds to a complete stoppage of molecular motion

Charles's Law, also known as the law of volumes, is an experimental gas law formulated by scientist Jacques Charles in the 1780s. It describes how gases tend to expand when heated. The 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 measured with the Kelvin scale. The Kelvin scale must be used because zero on the Kelvin scale, or absolute zero, corresponds to a complete stoppage of molecular motion. This temperature is equal to −273°C, and it is not possible to go lower than this.

Mathematically, the direct relationship of Charles's Law can be represented by the equation:

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

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. The equation shows that as the absolute temperature increases, the volume of the gas also increases in proportion.

Charles's Law can also be used to compare changing conditions for a gas. The mathematical relationship becomes:

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

Where:

• \(V_1\) and \(T_1\) are the initial volume and temperature of a gas
• \(V_2\) and \(T_2\) are the final volume and temperature

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 then heated to 71°C, the new volume of the balloon can be calculated using Charles's Law. The temperatures must first be converted to Kelvin:

\[ V_2 = \frac{V_1 \times T_2}{T_1} = \frac{2.20 \: \text{L} \times 344 \: \text{K}}{295 \: \text{K}} = 2.57 \: \text{L} \]

So, the volume of the balloon increases to 2.57 L as the temperature increases.

Charles's Law can be used to compare changing conditions for a gas

Charles's Law, also known as the law of volumes, describes how gases tend to expand when heated. It states that the volume of a given mass of gas varies directly with its absolute temperature when pressure is kept constant. The absolute temperature is the temperature measured in Kelvin. This is because zero on the Kelvin scale corresponds to a complete stoppage of molecular motion.

Mathematically, the direct relationship of Charles's Law can be represented by the following equation:

$$\frac{V}{T} = k$$

Where:

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

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

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, let's say we have a balloon filled to a volume of $2.20 \: \text{L}$ at a temperature of $22^\text{o} \text{C}$. If the balloon is then heated to a temperature of $71^\text{o} \text{C}$, we can use Charles's Law to find the new volume of the balloon.

First, we rearrange the equation algebraically to solve for $V_2$:

$$V_2 = \frac{V_1 \times T_2}{T_1}$$

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

$$V_2 = \frac{2.20 \: \text{L} \times 344 \: \text{K}}{295 \: \text{K}} \approx 2.57 \: \text{L}$$

So, the volume of the balloon increases as the temperature increases.

Charles's Law is a special case of the ideal gas law

Charles's Law, also known as the law of volumes, is a statement that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature if the pressure remains constant. The law was first suggested by the French physicist Jacques Charles in the late 1780s.

Charles's Law can be expressed as:

> Vi/Ti = Vf/Tf

Where:

• Vi = initial volume
• Ti = initial absolute temperature
• Vf = final volume
• Tf = final absolute temperature

It is important to note that the temperatures used in Charles's Law are absolute temperatures measured in Kelvin.

For example, if we have a balloon filled to a volume of 2.20 L at a temperature of 22°C, and we then heat it to a temperature of 71°C, we can use Charles's Law to find the new volume of the balloon. By rearranging the equation to solve for Vf, we can plug in the known quantities and find that the new volume of the balloon is 2.57 L.

Charles's Law can also be used in various real-life applications, such as pop-up turkey thermometers and car engines.

Charles's Law has a wide range of applications in daily life

Charles's Law, also known as the Law of Volumes, is an experimental gas law that describes the relationship between the volume of a given mass of gas and its temperature when pressure is kept constant. The law states that the volume of a gas is directly proportional to its temperature. In other words, as the temperature of a gas increases, so does its volume, and vice versa.

Hot Air Balloons

The principle behind hot air balloons is based on Charles's Law. The envelope of a hot air balloon stores heated air, which increases in volume as the temperature rises, according to the law. As a result, the density of the air inside the envelope becomes lower than the density of the outside atmosphere, creating a buoyant force that lifts the balloon into the sky.

Baking

Charles's Law is also relevant in baking. Yeast is commonly used in bakery products like bread and cakes to make them soft and spongy. During the baking process, yeast produces carbon dioxide gas, which expands at high temperatures. This expansion contributes to the fluffy and spongy texture of the baked goods.

Soda Cans

Charles's Law explains why a chilled soda can has fewer bubbles compared to a warmer one. In a chilled can, the low temperature leads to a decrease in volume, resulting in fewer visible bubbles. Conversely, a warmer can has a higher temperature, causing an increase in volume and the spillover of bubbles when opened.

Deodorant Bottles

Deodorant bottles often come with warnings to protect them from sunlight and high temperatures. Charles's Law explains why this is necessary. Under high temperatures, the gas molecules inside the bottle expand, which can lead to the bursting of the bottle.

Automotive Engines

Charles's Law is also applicable in automotive engines, specifically in the power strokes of spark-ignition and compression-ignition engines. In spark ignition, the combustion gases are exposed to high temperatures, leading to an increase in their volume. This expansion increases the force against the cylinder and piston head, resulting in the rotation of the crankshaft. In diesel engines, compressed air is heated and combined with diesel fuel, leading to ignition.

Charles's Law, discovered by French physicist Jacques Charles, provides valuable insights into the behaviour of gases and has practical applications in various aspects of our daily lives.

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