Chapter 1.4, Problem 21PP

(a)

To determine

Plot the mass versus volume and draw the curve by the points.

Explanation of Solution

Given Information:

The mass and volume is given below.

Volume $\left({\text{cm}}^3\right)$	Mass $\left(\text{g}\right)$
1.0	19.4
2.0	38.6
3.0	58.1
4.0	77.4
5.0	96.5

The curve obtained by plotting the mass versus volume is given below.

  

(b)

To determine

Description of the resulting curve.

Explanation of Solution

The resulting curve is a straight line with volume on the horizontal axis and the mass on the vertical axis.

(c)

To determine

The relationship between the mass of pure gold nugget and the volume of the gold.

Explanation of Solution

The mass of the pure gold nugget varies linearly with the volume with the gold. The linear relationship exists between the mass of the pure gold and volume of the gold.

(d)

To determine

The slope of the graph.

Answer to Problem 21PP

The slope of the graph is $19.2\text{g}/{\text{cm}}^3$ .

Explanation of Solution

Given info:

First reading of the mass of the gold, $M_1=19.4\text{g}$ .

Second reading of the mass of the gold, $M_2=38.6\text{g}$ .

First reading of the volume of the gold, $V_1=1{\text{cm}}^3$ .

Second reading of the volume of the gold, $V_2=2{\text{cm}}^3$ .

Formula Used:

The expression for the slope of the curve is,

  $m=\frac{M_2-M_1}{V_2-V_1}$

Calculation:

Substitute the values in the above expression.

  $\begin{array}{c}m=\frac{38.6\text{g}-19.4\text{g}}{2{\text{cm}}^3-1{\text{cm}}^3}\\ =19.2\text{g}/{\text{cm}}^3\end{array}$

Therefore, the slope of the curve is $19.2\text{g}/{\text{cm}}^3$ .

(e)

To determine

The equation showing the mass as a function of the volume of the gold.

Answer to Problem 21PP

The equation of the mass as a function of the volume of the gold is $M=mV+c$ .

Explanation of Solution

Formula Used:

The expression for the equation of the straight line is given as,

  $y=mx+c$

Here,

• $y$ is the quantity on the vertical axis.
• $x$ is the quantity on the horizontal axis.
• $c$ is the constant.

Calculation:

Substitute the values in the above expression.

  $M=mV+c$

Therefore, the equation of the mass as a function of the volume of the gold is $M=mV+c$ .

(f)

To determine

The word interpretation of the slope of the line.

Explanation of Solution

The mass of the gold is the product of volume and density. So, it shows a line with density of the gold as the slope of the line. The slope of the line interprets the density of the gold.