Chapter 14.2, Problem 14SP

Interpretation Introduction

Interpretation: To determine the temperature when the volume is constant.

Concept Introduction: A gas law known as Gay-law Loussac states that a gas's pressure (when held at a constant volume as well as mass) has a direct relationship with its absolute temperature. In other words, while the mass is still fixed and the volume would be constant, the pressure gas is proportional to its temperature.

Answer to Problem 14SP

The temperature will be 3340K.

Explanation of Solution

The given data:

  ${\text{P}}_{\text{1}}$ = 198kPa

  ${\text{P}}_{\text{2}}$ = 225kPa

  ${\text{T}}_{\text{1}}$ = $\text{27}\text{+}\text{273}\text{=}\text{300K}$

  ${\text{T}}_{\text{2}}$ = ?

The temperature can be determined by using the formula:

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

Now, put the values of the given data in the above equation.

  $\begin{array}{l}\frac{{\text{P}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}}{{\text{T}}_{\text{2}}}\\ {\text{T}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{×T}}_{\text{1}}}{{\text{P}}_{\text{1}}}\\ {\text{T}}_{\text{2}}\text{=}\frac{\text{225×300}}{\text{198}}\\ {\text{T}}_{\text{2}}\text{=340 K}\end{array}$

Therefore, the temperature will be 340 K.