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
The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, and you need 50 rows of seats. (a) Write the sequence for the numb

If one acre costs $2500 how much does .39 of an acre cost?

how we will use the replacement problmes in our life?

Testing the hypothesis equality of two variances The test for equality of two population variances is based upon the variances in two independently chosen random samples drawn

differentiate x to the power 3

sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution)  sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(

do you guys have excel math

the variables x and y are thought to be related by a law of the form ay^2=(x+b)lnx Where a and b are unknown constants. Can a and b be found and how.


bunty and bubly go for jogging every morning. bunty goes around a square park of side 80m and bubly goes around a rectangular park with length 90m and breadth 60m.if they both take