Chapter 14, Problem 59A

Interpretation Introduction

Interpretation: To determine the mathematical expression for the combined gas law.

Concept Introduction: A theoretical gas called an ideal gas is made up of several independently moving point particles without any interparticle interactions. Because it adheres to the ideal gas rule, the ideal gas concept is helpful.

Answer to Problem 59A

The mathematical expression of the combined gas law will be $\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$

Explanation of Solution

Charles’s Law, Boyle's Law, and Gay Lussac's Law are combined into the Combined Gas Law. According to the Combined Gas Law, a gas's pressure, volume, and temperature must all be constant.

According to Boyles law:

  $\text{PV=K}\mathrm{.....}\text{(i)}$

According to Charles's law

  $\frac{\text{V}}{\text{T}}\text{=K}\mathrm{.......}\text{(ii)}$

By mixing equations (i) and (ii).

  $\frac{\text{PV}}{\text{T}}\text{=K}$

It can be expressed as:

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