Chapter U3.51, Problem 1TAI

Interpretation Introduction

Interpretation : Amount of water in equal volumes of snow and rain is to be determined.

Concept Introduction : Scientists measure the snowpack to predict the amount of water that will be available for consumption for the rest of year. The mountains get several feet of snow every winter and this snow melts and reaches the reservoir. Rain and snow can be measured in inches.

Answer to Problem 1TAI

If the volume of snow and rain water is equal, mass of snow will be less than mass of rain water because density of snow is less than density of water.

Explanation of Solution

When snow melts its volume decreases but its mass remains the same. This is because the same water molecules are present in frozen snow and melted snow. Density of snow is less than density of water.

The formula to calculate mass of a substance is given by:

  $\begin{array}{l}\text{Mass(m)=Density(D)×Volume(V)}\\ \text{m=D×V}\end{array}$

To calculate mass of snow;

  $\text{m(snow)=D(snow)×V(snow)}$

To calculate mass of rain water;

  $\text{m(rain)=D(rain)×V(rain)}$

Since $\text{D(snow)<D(rain)}$ and $\text{V(snow)=V(rain)}$

  $\text{m(snow)<m(rain)}$

Mass and volume are proportional to each other for a specific substance.

Therefore, if the volume of snow and rain water is equal, mass of snow will be less than mass of rain water.

Conclusion

Mathematical equations can be used to calculate volume or mass of snow and rain water. To use mathematical equations, we must know the density of snow and density of liquid water.