Exploring Gas Volume Changes with Charles's Law: A Step-by-Step Guide

Understanding how a gas's volume changes with temperature while maintaining constant pressure is crucial in many scientific and engineering applications. Charles's Law is one such law that describes this relationship. This article will explore how to use Charles's Law to calculate the new volume of a balloon when its temperature changes. We will walk through a detailed example using Charles's Law and convert temperatures from Celsius to Kelvin for accuracy.

Introduction to Charles's Law

Charles's Law is a fundamental principle in the field of thermodynamics, specifically dealing with the behavior of gases. According to Charles's Law, the volume of a gas is directly proportional to its absolute temperature when the pressure is held constant. Mathematically, this is represented by the formula:

V/T constant

This relationship can be expressed more explicitly as:

VV1/T1*T2

Understanding the Example

In the problem we are given, a balloon is initially in an air-conditioned room with a temperature of 27°C and a volume of 4.0 liters. The balloon is then heated to a final temperature of 57°C. Keeping the pressure constant, we need to find the new volume of the balloon.

Step-by-Step Calculation

Step 1: Convert Temperatures to Kelvin

The first step is to convert the temperatures from Celsius to Kelvin. The conversion formula is T(K) T(°C) 273.15.

Initial Temperature T_1 27°C 27 273.15 300.15 K Final Temperature T_2 57°C 57 273.15 330.15 K

Step 2: Use Charles's Law

Next, we will use Charles's Law to find the new volume. The formula for Charles's Law is:

V1/T1 V2/T2

Given:

Initial Volume V_1 4.0 L Initial Temperature T_1 300.15 K Final Temperature T_2 330.15 K

Substituting these values into the formula:

V2 V1 * T2 / T1

V2 4.0 L * 330.15 K / 300.15 K

V2 ≈ 4.0 L * 1.099 4.396 L

Final Answer: The new volume of the balloon when heated to 57°C is approximately 4.40 liters.

Revised Example with Clear Temperature Conversion

For a clearer example, let's solve a problem where the balloon is initially at 23°C and is heated to 39°C. We will keep the pressure constant and follow the same steps, but this time, we will ensure the temperatures are directly in Kelvin for the calculation.

Step 1: Convert Temperatures to Kelvin

Initial Temperature T_1 23°C 23 273.15 296.15 K

Final Temperature T_2 39°C 39 273.15 312.15 K

Step 2: Calculation Using Charles's Law

Given:

Initial Volume V 5 L Initial Temperature T_1 296.15 K Final Temperature T_2 312.15 K

Using the formula:

V_2 V_1 * T_2 / T_1

V_2 5 L * 312.15 K / 296.15 K

V_2 ≈ 5 L * 1.054 5.27 L

Final Answer: The new volume of the balloon when heated to 39°C is approximately 5.27 liters.

Final Analysis

Charles's Law is a powerful tool in understanding how gases behave under changing conditions. By converting temperatures to Kelvin and using the direct proportionality of volume to temperature, we can accurately predict how a gas will behave under different conditions. This principle is widely applicable in various fields, including atmospheric science, engineering, and even everyday life, such as adjusting balloon sizes for hot air balloons and party decorations.

Conclusion

Understanding Charles's Law and its application to gas volume changes can greatly enhance your ability to solve real-world problems. Whether it's adjusting the size of a balloon or understanding atmospheric pressure, this law provides a solid foundation for further exploration into the realm of thermodynamics.