Chapter 14.2, Problem 13SP

Interpretation Introduction

Interpretation: To determine the pressure if the volume does not change.

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 13SP

The final temperature will be 101.46 kPa.

Explanation of Solution

The formula which gave the relation between the pressure, volume, temperature as well as the number of moles, is named an ideal gas equation.

It can be represented by $\text{PV}\text{=}\text{nRT}$ .

Where P is pressure, V is volume, T is temperature, and n is the number of moles.

When the volume will be kept constant then the new expression will be

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

Where ${\text{P}}_{\text{1}}$ is initial pressure, ${\text{P}}_{\text{2}}$ is final pressure, ${\text{T}}_{\text{1}}$ is initial Temperature, ${\text{T}}_{\text{2}}$ is final Temperature.

Given data:

Initial Temperature= $\text{41+273=314K}$ .

Initial pressure ( ${\text{P}}_{\text{1}}$ ) = 108kPa

Final pressure ( ${\text{P}}_{\text{2}}$ ) = ?

Final Temperature = $\text{22+273=295K}$

Now, put the values of the given data in equation (i).

  $\begin{array}{c}\frac{{\text{P}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}}{{\text{T}}_{\text{2}}}\\ {\text{P}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{1}}{\text{×T}}_{\text{2}}}{{\text{T}}_{\text{1}}}\\ \text{=}\frac{\text{108×295}}{\text{314}}\\ \text{=101}\text{.46kPa}\end{array}$

Therefore, the final temperature will be 101.46kPa