Understanding Gas Behavior Under Constant Pressure: A Real-World Application

In this article, we will explore a real-world problem involving the behavior of a gas under constant pressure. Specifically, we will analyze how the temperature of a gas changes when its volume expands. We will also introduce Charles' Law and the Ideal Gas Law, which are fundamental principles in understanding gas behavior. The article provides a step-by-step solution to a given problem and explains the significance of using the correct temperature scale.

Problem Statement: Gas Under Constant Pressure

A gas at 25°C and 0.987 atm pressure is confined in a cylinder by a piston. When the cylinder is heated, the gas volume expands from 0.250 L to 16.5 L. To find the new temperature of the gas in Kelvin, assuming the pressure is constant, we need to carefully apply the principles of gas behavior under these conditions.

Let's break down the solution to this problem:

1. Constants and Assumptions: We assume the gas exhibits ideal behavior, and the pressure remains constant.

2. Applicable Laws: The ideal gas law (P1V1/T1 P2V2/T2) and Charles' Law (V1/V2 T1/T2) are relevant here. Since the pressure is constant, we can simplify the ideal gas law to V1/T1 V2/T2.

Solution to the Problem

Step-by-Step Solution:

Convert the initial temperature to Kelvin: T1 (initial temperature in Kelvin) is calculated as follows: T1 25°C 273.15 298.15 K. Substitute the given values into the equation: V1 0.250 L, V2 16.5 L, and T1 298.15 K. Using Charles' Law, the equation becomes: Evaluate the final temperature (T2):

V1/T1 V2/T2

0.250 L / 298.15 K 16.5 L / T2

Solving for T2, we get:

T2 (16.5 L * 298.15 K) / 0.250 L

T2 ≈ 19668.75 K

Discussion: Practical Implications

The calculated temperature (19668 K) may seem extremely high compared to everyday experiences. However, let's break it down:

Theoretical Insight: Under constant pressure (0.987 atm), the gas volume expands significantly (16.5 / 0.250 66 times). Consequently, the temperature also increases dramatically, leading to the high value of 19668 K. Comparison with Actual Examples: On the surface of the sun, the temperature is approximately 5778 K. Therefore, the calculated temperature is far exceeding the surface temperature of the sun. Real-World Application: While the example provided is highly unrealistic, it serves as a powerful demonstration of the principles behind gas behavior under constant pressure.

Conclusion

The behavior of gases under constant pressure is governed by fundamental laws, such as Charles' Law and the Ideal Gas Law. Our analysis has shown that when a gas expands significantly under constant pressure, its temperature also increases correspondingly. This understanding is crucial in various scientific and engineering applications, such as thermodynamics, atmosphere science, and industrial processes.

Keywords

Charles' Law, Ideal Gas Law, Gas Temperature Calculation