Determining Volume of Gas at Different Temperatures: A Practical Application of Charles's Law

When a fixed mass of gas is heated at constant pressure, the volume of the gas changes with the temperature. This principle, known as Charles's Law, is a fundamental concept in thermodynamics. In this article, we will explore how to calculate the volume of a gas at a different temperature using Charles's Law. This is particularly useful for students and professionals in physics, chemistry, and engineering.

A Step-by-Step Guide to Using Charles's Law

Charles's Law, which states that the volume of a gas is directly proportional to its absolute temperature when the pressure is constant, provides a straightforward way to solve such problems. The formula for Charles's Law is given by:

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

Given Data

V1 600 cm3 T1 0 °C 273.15 K T2 10 °C 283.15 K

Calculation Steps

Step 1: Substitute the known values into the formula.

[ frac{600 , text{cm}^3}{273.15 , text{K}} frac{V_2}{283.15 , text{K}} ]

Step 2: Solve for V2.

Cross-multiply to solve for V2:
[ 600 , text{cm}^3 times 283.15 , text{K} V_2 times 273.15 , text{K} ]
[ V_2 frac{600 , text{cm}^3 times 283.15 , text{K}}{273.15 , text{K}} ]

Step 3: Calculate V2 using a calculator or a computational tool.

[ V_2 approx frac{600 times 283.15}{273.15} approx 621.26 , text{cm}^3 ]

Conclusion

The volume of the gas at 10 degrees Celsius is approximately 621.26 cm3.

Further Examples and Applications

Understanding Charles's Law is crucial for various applications in physics and engineering. Here are a few scenarios and calculations that illustrate the use of Charles's Law:

Example 1

A fixed mass of gas has an initial volume of 700 cm3 at 25 °C (298.15 K). If the temperature is increased to 100 °C (373.15 K) under constant pressure, what is the new volume of the gas?

Given: V1 700 cm3, T1 298.15 K, T2 373.15 K

Solution:

[ frac{700}{298.15} frac{V_2}{373.15} ]

[ V_2 frac{700 times 373.15}{298.15} approx 860.7 , text{cm}^3 ]

Example 2

Consider a gas with an initial volume of 550 cm3 at 15 °C (288.15 K). The gas is cooled until its volume is 450 cm3. What is the final temperature of the gas?

Given: V1 550 cm3, T1 288.15 K, V2 450 cm3

Solution:

[ frac{550}{288.15} frac{450}{T_2} ]

[ T_2 frac{450 times 288.15}{550} approx 220.68 , text{K} ]

Key Concepts and Formulas

Charles's Law: ( frac{V_1}{T_1} frac{V_2}{T_2} ) Temperature Conversion from Celsius to Kelvin: ( T(K) T(°C) 273.15 )

References and Further Reading

To deepen your understanding of gas laws, consider exploring the following resources:

LibreTexts on Charles's Law Khan Academy on Gas Laws