Exploring the Relationship Between Volume and Temperature: A Gas Balloon Example

When dealing with gases, understanding the relationship between volume and temperature is crucial. A fundamental equation used to analyze such relationships is the ideal gas law:

PV nRT

where:

P pressure of the gas V volume of the gas n number of moles of gas R ideal gas constant T temperature (in Kelvin)

During our exploration, we can rearrange the ideal gas law to isolate volume:

V frac{nRT}{P}

This equation indicates that the volume (V) of a gas is directly proportional to its temperature (T) when the pressure (P) and the number of moles (n) are constant.

Applying Charles's Law to a Gas Balloon

Let's consider the scenario where a gas balloon has a volume of 1.40 liters at 20°C. If the temperature is increased to 25°C with the pressure remaining constant, how will the volume of the gas change?

A Step-by-Step Analysis

Converting Temperatures to Kelvin: The gas law uses temperatures in Kelvin (K), so we need to convert the given temperatures. Initial Conditions: At 20°C, T1 20°C 273.15 293.15 K. Final Conditions: At 25°C, T2 25°C 273.15 298.15 K. Identifying Constants and Variables: We assume the pressure remains the same (P) and the number of moles (n) of the gas do not change. Therefore, we use Charles's law, a specific case of the ideal gas law, which states that the volume of a gas is directly proportional to its temperature when pressure and amount of gas are constant: Using the Ideal Gas Law: For the initial state: V? frac{nRT?}{P} For the Final State: V? frac{nRT?}{P} Setting Up the Proportion: Since n, R, and P are constant, we can simplify the proportionality: V? / T? V? / T? Substituting Known Values: We can now substitute the known values to find the new volume V?.

Calculations

From our initial conditions: V? 1.40 L and T? 293.15 K.

From our final conditions: T? 298.15 K.

Using the formula for volume-temperature proportionality:

V? V? * frac{T?}{T?}

Substituting the values:

V? 1.40 L * frac{298.15 K}{293.15 K}

This simplifies to:

V? 1.40 L * 1.0169

Therefore, the volume at 25°C is approximately:

V? 1.423 L

Conclusion

By understanding and applying the ideal gas law, we can predict and calculate changes in the volume of a gas under specific conditions. In this example, the volume of the gas balloon increases from 1.40 L to 1.423 L as the temperature rises from 20°C to 25°C, with constant pressure. This analysis highlights the direct proportionality between temperature and volume in gases, a principle rooted in Charles's Law.

Further Reading and Learning

Explore more about gas laws, Charles's Law, and the relationship between volume and temperature in various conditions. Understanding these principles is crucial for advanced studies in chemistry, physics, and engineering.