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Chapter 5: Problem 38

Graphical curves that explain Boylc's law are called (1) Isobars (2) Iscohores (3) Isotherms (4) Isomers

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Isotherms

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01

Understand Boyle's Law

Boyle's Law states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, it can be expressed as \( PV = k \), where \( P \) represents pressure, \( V \) represents volume, and \( k \) is a constant.
02

Identify the Variables

The core variables in Boyle's Law are pressure (\( P \)) and volume (\( V \)), while temperature remains constant.
03

Interpret Graphical Curves

Graphical curves that represent the relationship in Boyle's Law typically show how pressure and volume change while keeping temperature constant.
04

Define 'Isotherms'

The term 'isotherms' refers to curves on a graph that represent the same temperature. Since Boyle's Law examines pressure and volume at constant temperature, these curves are isothermal.
05

Match the Definition

Among the given options, 'isotherms' (option 3) correctly describes the graphical curves that explain Boyle's Law.

Key Concepts

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

Graphical Curves
Graphical curves in the context of Boyle's Law help visualize the relationship between pressure and volume of a gas at constant temperature. These curves make it easier to understand how changing one variable affects the other.
When we plot pressure (P) on the y-axis and volume (V) on the x-axis, the curve we get is hyperbolic in nature. This means that as the volume increases, the pressure decreases, and vice versa.
Remember, these curves only make sense when the temperature remains constant. This constancy is a key feature of understanding Boyle's Law through graphical representation.
Pressure-Volume Relationship
Boyle's Law clearly states that pressure and volume are inversely proportional to each other. This inverse relationship means that if the volume of a gas increases, the pressure decreases, provided the temperature remains constant.
Mathematically, this relationship is expressed as: \[ PV = k \] where:
  • \( P \) stands for pressure
  • \( V \) stands for volume
The product of pressure and volume is always constant (\( k \)) for a given amount of gas at a constant temperature.
For instance, if you start with a volume \( V_1 \) and pressure \( P_1 \), and then change to a new volume \( V_2 \), the new pressure \( P_2 \) can be calculated because \( P_1V_1 = P_2V_2 \). This relationship is fundamental in fields such as chemistry and physics, where understanding gas behaviors is crucial.
Isotherms
An isotherm is a curve representing the pressure-volume relationship of a gas at a constant temperature. When studying Boyle's Law, isotherms are essential, as they depict how pressure and volume vary while maintaining the same temperature.
Each isotherm corresponds to a different temperature. For a single temperature, the isotherm will show the inverse nature of the pressure-volume relationship.
Think of an isotherm as a snapshot of the gas behavior at a particular, unchanging temperature. Plotting multiple isotherms on the same graph can give insights into how gas behavior changes with different temperatures. However, Boyle's Law specifically focuses on one isotherm at a time since it deals with constant temperature scenarios.

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