Chapter 14.2, Problem 16SP

Interpretation Introduction

Interpretation: To determine the value of new pressure.

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

Answer to Problem 16SP

The amount of pressure will be 128.5KPa

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:

  $\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}\mathrm{......}\text{(i)}$

The given data:

  ${\text{V}}_{\text{1}}$ = 5L

  ${\text{V}}_{\text{2}}$ = 7L

  ${\text{T}}_{\text{1}}$ = ${\text{-50}}^{\text{ο}}\text{C+273}\text{=}\text{223K}$

  ${\text{T}}_2$ = ${\text{102}}^{\text{ο}}\text{C+273}\text{=}\text{375K}$

  ${\text{P}}_{\text{1}}$ =107KPa

Put the values of the given data in equation (i).

  $\begin{array}{c}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}\\ {\text{P}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{T}}_{\text{2}}}{{\text{V}}_{\text{2}}{\text{T}}_{\text{1}}}\\ {\text{P}}_{\text{2}}\text{=}\frac{\text{107×5×375}}{\text{7×223}}\\ \text{=128}\text{.5KPa}\end{array}$

Therefore, the amount of pressure will be 128.5KPa.