Chapter 14.2, Problem 23LC

Interpretation Introduction

Interpretation: To derive the Charles law from the combined gas law.

Concept Introduction: Ideal gas equation give the relation between temperature, pressure, and volume. The ideal gas equation can be shown as. $\text{PV}\text{=}\text{nRT}$ . Pressure and volume will be directly proportional to one another.

Answer to Problem 23LC

The Charles law equation will be $\frac{{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$ .

Explanation of Solution

Combined gas law gave the relation between the pressure, volume, and temperature. If a gas has initial pressure ${\text{P}}_{\text{1}}$ after some time its pressure gets changed into ${\text{P}}_{\text{2}}$ .

By giving ${\text{T}}_{\text{1}}$ temperature, its volume will be ${\text{V}}_{\text{1}}$ and By giving ${\text{T}}_2$ temperature, its volume will be ${\text{V}}_{\text{2}}$ , It can be written as the formula:

  $\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$

It is known that in Charles's law pressure will be constant. It can be shown as:

  $\frac{{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$