Chapter 5, Problem 12STP

Interpretation Introduction

Interpretation:

The approximate rate of heating in degrees per second and in degrees per minute needs to be determined using the graph plotted between temperature and time.

Temperature of water with heating
Time (s)	Temperature (ºC)
0	16.3
30	19.7
60	24.2
90	27.8
120	32.0
150	35.3
180	39.6
210	43.3
240	48.1

Concept introduction:

The difference and trend in the data can be easily visualized via plotting graphs. This can be said that a visual display of data is its graph. There are three types of graphs:

• The parts of a fixed whole can be represented by a circle graph. The different parts are represented as percents where the entire circle represents $100\%$.
• The variation of a quantity across different categories can be represented by a bar graph.
• In the line graph, the intersection of data for two variables is represented by the different points.

Answer to Problem 12STP

The rate of heating in degree per second is $0.1313°\text{C/s}$ and this value in degree per minute is $7.878°\text{C/min}$.

Explanation of Solution

The difference and trend in the data can be easily visualized via plotting graphs. This can be said that a visual display of data is its graph.

The graph showing temperature versus time is as follows:

Now, for the determination of the slope, divide the difference of the two points on y-axis by the difference of the two points on x-axis.

Also, the straight line equation can be drawn on the graph.

Form the graph, the equation of straight line is as follows:

$y=0.1313x+16.058$

On comparing with:

$y=mx+c$

The slope is $0.1313°\text{C/s}$. Therefore the rate of heating is $0.1313°\text{C/s}$.

To convert the above value in $°\text{C/s}$ to $°\text{C/min}$, multiply by 60 seconds per minute as:

$\frac{0.1313°\text{C}}{\text{s}}\times \frac{60\text{s}}{1\min }=7.878°\text{C/min}$

Hence, the value in degree per minute is $7.878°\text{C/min}$.

Conclusion

The rate of heating in degree per second is $0.1313°\text{C/s}$ and this value in degree per minute is $7.878°\text{C/min}$.