Charles’s Law: A Comprehensive Guide for Science Students

Charles’s Law is a fundamental principle in thermodynamics that describes the relationship between the volume and temperature of a gas at constant pressure. This 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, which starts at absolute zero, the temperature at which molecular motion ceases.

Understanding the Equation of Charles’s Law

Mathematically, Charles’s Law can be represented by the equation:

V/T = k

Where:
– V is the volume of the gas
– T is the absolute temperature of the gas
– k is a constant for a given gas sample

This equation can be rearranged to:

V1/T1 = V2/T2

Where:
– V1 and T1 are the initial volume and temperature of the gas
– V2 and T2 are the final volume and temperature of the gas

This equation can be used to calculate any one of the four quantities (volume or temperature) if the other three are known.

Practical Application of Charles’s Law

Let’s consider an example to understand the practical application of Charles’s Law:

Suppose a balloon is filled with a volume of 2.20 L at a temperature of 22°C, and then heated to a temperature of 71°C. We can use Charles’s Law to calculate the new volume of the balloon.

First, we need to convert the initial temperature from Celsius to Kelvin:
– 22°C + 273 = 295 K

Then, we can use the equation V1/T1 = V2/T2 to solve for the new volume:
– V2 = V1(T2/T1)
– V2 = 2.20 L × (344 K / 295 K)
– V2 = 2.62 L

Therefore, the new volume of the balloon after heating to 71°C is 2.62 L.

Graphical Representation of Charles’s Law

When the relationship between the volume and temperature of a gas at constant pressure is graphed, it results in a straight line that passes through the origin. This indicates a direct relationship between the two variables.

The slope of the line is equal to the constant k, which is equal to the volume divided by the absolute temperature.

Practical Applications of Charles’s Law

Charles’s Law has numerous practical applications, including:

1. Pressure Cookers: The increased temperature inside a pressure cooker causes the volume of the gas (air) to expand, leading to an increase in pressure. This higher pressure allows the cooking temperature to be raised, resulting in faster cooking times.

2. Tire Inflation: The volume of air in a tire increases as the temperature rises, causing the tire pressure to increase. This is why it’s important to check tire pressure when the tires are cold, as the pressure will be lower than when the tires are warm.

3. Atmospheric Pressure Measurement: Charles’s Law can be used to measure atmospheric pressure by observing the volume of a gas at a known temperature.

4. Thermometers: Some types of thermometers, such as the constant-volume gas thermometer, rely on the principles of Charles’s Law to measure temperature.

5. Balloons and Airships: The expansion of gases due to increased temperature is the basis for the operation of hot air balloons and airships.

Limitations and Assumptions of Charles’s Law

While Charles’s Law is a powerful tool for understanding the behavior of gases, it is important to note that it has certain limitations and assumptions:

1. Constant Pressure: Charles’s Law is only valid when the pressure of the gas is kept constant.
2. Ideal Gas Behavior: The law assumes that the gas behaves as an ideal gas, which means that the gas particles do not interact with each other and occupy negligible volume compared to the total volume of the gas.
3. Small Temperature Ranges: Charles’s Law is most accurate for small temperature ranges, as the relationship between volume and temperature may become non-linear at larger temperature differences.

Numerical Problems and Examples

1. Problem: A gas has a volume of 2.5 liters at 20°C. What will the volume of the gas be at 40°C, assuming constant pressure?

Solution:
– Initial volume (V1) = 2.5 liters
– Initial temperature (T1) = 20°C + 273 = 293 K
– Final temperature (T2) = 40°C + 273 = 313 K
– Using the equation V1/T1 = V2/T2, we can solve for the final volume (V2):
– V2 = (V1 × T2) / T1
– V2 = (2.5 liters × 313 K) / 293 K
– V2 = 2.67 liters

1. Problem: A gas has a volume of 1.5 liters at 0°C. What will the volume of the gas be at 100°C, assuming constant pressure?

Solution:
– Initial volume (V1) = 1.5 liters
– Initial temperature (T1) = 0°C + 273 = 273 K
– Final temperature (T2) = 100°C + 273 = 373 K
– Using the equation V1/T1 = V2/T2, we can solve for the final volume (V2):
– V2 = (V1 × T2) / T1
– V2 = (1.5 liters × 373 K) / 273 K
– V2 = 2.05 liters

1. Problem: A gas has a volume of 3 liters at 25°C. What is the temperature at which the gas will have a volume of 4 liters, assuming constant pressure?

Solution:
– Initial volume (V1) = 3 liters
– Initial temperature (T1) = 25°C + 273 = 298 K
– Final volume (V2) = 4 liters
– Using the equation V1/T1 = V2/T2, we can solve for the final temperature (T2):
– T2 = (V2 × T1) / V1
– T2 = (4 liters × 298 K) / 3 liters
– T2 = 397 K
– T2 - 273 = 124°C

Conclusion

Charles’s Law is a fundamental principle in thermodynamics that describes the relationship between the volume and temperature of a gas at constant pressure. By understanding the mathematical equation, graphical representation, and practical applications of this law, science students can gain a deeper understanding of the behavior of gases and their role in various scientific and engineering applications.

References:

1. 3 Ways to Demonstrate Charles’s Law – wikiHow
2. 8.1: Charles’s Law- Volume and Temperature – Chemistry LibreTexts
3. Charles’s Law and Absolute Zero – Flinn Scientific
4. 11.5: Charles’s Law- Volume and Temperature – Chemistry LibreTexts