Cartesian graph of density of water - temperature, Mathematics

Cartesian Graph of Density of Water - Temperature:

Example: The  density  of  water  was  measured  over  a  range  of  temperatures.   Plot the subsequent recorded data on a Cartesian coordinate graph.

Temperature (°C)                                                       Density (g/ml)

40°                                                                                0.992

50°                                                                                0.988

60°                                                                                0.983

70°                                                                                0.978

80°                                                                                0.972

90°                                                                                0.965

100°                                                                              0.958

To plot the data the first step is to label the x-axis and the y-axis. Let the x-axis be temperature in °C and the y-axis is density in g/ml.

The further step is to establish the units of measurement along every axis. The x-axis must range from approximately 40 to 100 and the y-axis from 0.95 to 1.00.

The points are then plotted one by one.  Below figure shows the resulting Cartesian coordinate graph.

2408_Cartesian Graph of Density of Water - Temperature.png

Figure: Cartesian Coordinate Graph of Density of Water vs. Temperature

Graphs are convenient since, at a single glance, the main features of the relationship among the two physical quantities plotted can be seen.  Further, if some previous knowledge of the physical system under consideration is available, the numerical value pairs of points could be connected through a straight line or a smooth curve. From these plots, a values at points not specifically measured or calculated can be acquired.  In Figures, the data points have been connected through a straight line and a smooth curve, correspondingly.  From these plots, the values at points not particularly plotted can be determined. For instance, using Figure, the density of water at 65°C can be determined to be 0.98 g/ml.  Because 65°C is within the scope of the available data, it is known as an interpolated value.   Also using Figure, the water density at 101°C can be estimated to be 0.956 g/ml.  Because 101°C is outside the scope of the available data, it is known as an extrapolated value.  While the value of 0.956 g/ml appears reasonable, a significant physical fact is absent and not predictable from the data given.  Water boils at 100°C at atmospheric pressure.  At temperatures above 100°C it is not a liquid, but a gas.  Thus, the value of 0.956 g/ml is of no importance except when the pressure is above atmospheric.

This describes the relative ease of interpolating & extrapolating using graphs. It also points out the precautions which must be taken, namely, extrapolation & interpolation should be done only if there is some prior knowledge of the system. That is particularly true for extrapolation where the available data is being extended into a region whereas unknown physical changes may take place.

Posted Date: 2/9/2013 5:32:45 AM | Location : United States







Related Discussions:- Cartesian graph of density of water - temperature, Assignment Help, Ask Question on Cartesian graph of density of water - temperature, Get Answer, Expert's Help, Cartesian graph of density of water - temperature Discussions

Write discussion on Cartesian graph of density of water - temperature
Your posts are moderated
Related Questions
In a frequency distribution mode is 7.88, mean is 8.32 find the median.  (Ans: 8.17) Ans:  Mode = 3 median - 2 mean 7.88 = 3 median - 2 x 8.32 7.88 +16.64 = 3 median

what is the meaning of volume of plane figures?

Find out the least number of cables required to connect 100 computers to 20 printers to assurance that 20 computers can directly access 20 different printers.  Justify your answer.

Simplify following. Suppose that x, y, & z are positive.                      √ y 7 Solution In this case the exponent (7) is larger than the index (2) and thus the fir


#questio Study A Study B Study C x2 = 1.683 F = 7.357 r = .83 df = 4

Geometric mean - It is a measure of central tendency normally utilized to measure industrial increases rates. - It is explained as the nth root of the product of 'n' observa

Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures

i dont know how to do probobility iam so bad at it

Method to solve Simultaneous Equations with two or more than two variables Method  Above we have seen equations wherein we are required to find the value of the