Chapter 3, Problem 105A

Interpretation Introduction

Interpretation : The mass of air in kilograms is to be calculated.

Concept Introduction : The measure of how densely a material is packed together is called density. It is described as the mass per unit volume.

Answer to Problem 105A

The mass of air in kilograms is $1800\text{kg}$ .

Explanation of Solution

Given information:

The density of air is $1.20\text{g/L}$ .

The room has dimensions of $25\text{m}$ by $\text{15}\text{m}$ by $\text{4}\text{m}$ .

The connectivity between mass and volume is density. The formula of mass when density and volume are given:

  $\text{Mass}\text{=}\text{Density}\times \text{Volume}$

To calculate the mass of air, first, need to find the volume of air using its dimensions.

The volume is given as

  $\begin{array}{c}\text{Volume}=l\times b\times h\\ =25\text{m}\times \text{15}\text{m}\times \text{4}\text{m}\\ \text{=1500}{\text{m}}^3\end{array}$

To calculate the mass of air, substitute the values in the mass formula:

  $\begin{array}{c}\text{Mass}\text{=}\text{Density}\times \text{Volume}\\ =\frac{1.20\cancel{\text{g}}}{\cancel{\text{L}}}\times 1500\cancel{{\text{m}}^3}\times \frac{\cancel{{10}^3}\cancel{\text{L}}}{\cancel{{\text{m}}^3}}\times \frac{1\text{kg}}{\cancel{{10}^3}\cancel{\text{g}}}\left(\because 1{\text{m}}^3={10}^3\text{L,}\text{1}\text{kg}\text{=}{\text{10}}^3\text{g}\right)\\ =1800\text{kg}\end{array}$

The mass is $1800\text{kg}$ .