Chapter U3.51, Problem 1E

Interpretation Introduction

Interpretation : Use of mathematical equations to convert volume of snow in a snowpack to the volume of water in the snowpack is to be explained.

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.When snow melts, its volume decreases but its mass remains the same.

Answer to Problem 1E

Mass of snow can be calculated by;

  $\text{m(snow)=D(snow)×V(snow)}$

Mass of rain water is equal to mass of snow

  $\text{m(snow)=m(rain)}$

One can calculate volume of rain water as;

  $\text{V(rain)=}\frac{\text{m(rain)}}{\text{D(rain)}}$

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. One can use density equation to convert between mass and volume.

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

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

Massof snow can be calculated by;

  $\text{m(snow)=D(snow)×V(snow)}$

Mass of rain water is equal to mass of snow as same amount of snow melts to form liquid water.

$\text{m(snow)=m(rain)}$

Since, the density of water is $\text{1}\text{.0g/mL}$

One can calculate volume of rain water as by using the following equation;

  $\text{V(rain)=}\frac{\text{m(rain)}}{\text{D(rain)}}$

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.