Problem 6 What relationship does Charles's... [FREE SOLUTION]

Chapter 12: Problem 6

What relationship does Charles's law express?

Short Answer

Expert verified

Charles's law expresses the direct proportional relationship between the volume and absolute temperature of a gas, provided the pressure is constant. It is mathematically represented by the formula, \( V = kT \) or \( V_1/T_1 = V_2/T_2 \), where \( V \) is the volume of the gas, \( T \) is the absolute temperature, and \( k \) is the constant of proportionality.

Step by step solution

Understanding Charles's law

Charles's law, also known as the law of volumes, describes how gases tend to expand when heated. It is considered as a basic principle in the study of physical chemistry and thermodynamics.

Statement of Charles's law

The formal statement of Charles's Law can be framed as follows: 'The volume of a given amount of gas is directly proportional to its absolute temperature on the Kelvin scale, provided its pressure remains constant.'

Expressing the law mathematically

The mathematical representation of Charles's law is \( V \propto T \), where \( V \) is the volume of the gas, and \( T \) is the absolute temperature. When the constant of proportionality is included, the law can also be stated as \( V = kT \), where \( k \) is the constant of proportionality. Since both the conditions, volume and temperature remain constant, the law can also be expressed as \( V_1/T_1 = V_2/T_2 \) for any two sets of corresponding volume-temperature measurements of the gas.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gas Laws

Gas laws are a set of principles that describe the behavior of gases. They help us understand how gases respond to various changes in pressure, temperature, and volume. These laws are crucial for predicting how gases will act under different conditions.

Boyle's Law: This law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This means if you decrease the volume of a gas, its pressure increases, and vice versa.
Charles's Law: As we focus on here, it delineates the relationship between volume and temperature.
Avogadro's Law: It indicates that the volume of a gas is directly proportional to the number of moles if temperature and pressure are constant.

These laws together form the ideal gas law, a fundamental equation in chemistry that links pressure, volume, temperature, and moles of gas in a single formula: \( PV = nRT \), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature.

Thermodynamics

Thermodynamics is the study of heat and energy transfer, a critical branch of physics that explores how energy is converted between heat and work. It applies to gases and explains principles like Charles's Law.
The core of thermodynamics lies in its four fundamental laws:

First Law (Conservation of Energy): Energy cannot be created or destroyed, only transformed from one form to another.
Second Law: Heat naturally flows from hot to cold bodies, introducing the concept of entropy, or disorder, in a system.
Third Law: As temperature approaches absolute zero, the entropy of a system approaches a minimum value.

Charles's Law is involved in thermodynamics as it relates how temperature influences the volume of a gas, which in turn ties into energy concepts. In essence, as a gas absorbs heat, it tends to expand, increasing its volume while maintaining the same pressure.

Temperature and Volume Relationship

The temperature and volume relationship in gases is a fundamental concept in thermodynamics and is specifically described by Charles's Law. This relationship highlights how gases behave when subjected to temperature changes while keeping the pressure constant.

According to Charles's Law, when the temperature of a gas increases, its volume increases proportionally. This means that for a constant pressure situation, heating a gas will cause it to expand.
Mathematically, this is expressed as \( V/T = k \) or \( V_1/T_1 = V_2/T_2 \), where \(V\) is volume and \(T\) is temperature in Kelvin. \(k\) is a constant that signifies the proportionality between these two properties for a given sample of gas.
This principle explains everyday phenomena, like why a balloon inflates when heated or why car tires can overinflate on a hot day.

Understanding this relationship not only aids in solving gas law problems but also gives insight into how gas-based systems operate in real-life scenarios.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

What relationship does Charles's law express?

Short Answer

Step by step solution

Understanding Charles's law

Statement of Charles's law

Expressing the law mathematically

Key Concepts

Gas Laws

Thermodynamics

Temperature and Volume Relationship

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Chemical Analysis

Ionic and Molecular Compounds

Organic Chemistry

Chemistry Branches

Making Measurements

Study anywhere. Anytime. Across all devices.