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
Describe Common Phrases to Represent Math Operations? The table below shows the common phrases used in word problems to represent addition, subtraction, multiplication, and div

what is 9/16 Divided by 7/8

give me the derivation of external division of sectional formula using vectors

interestind topic in operation research for doing project for msc mathematics

A shuttlecock used for playing badminton has the shape of a frustum of a Cone mounted on a hemisphere.  The external diameters of the frustum are 5 cm and 2 cm, and the height of t

S olve the subsequent IVP. dv/dt = 9.8 - 0.196v;               v(0) = 48 Solution To determine the solution to an Initial Value Problem we should first determine the gen

Project part A, part B, part C

Find out the x-y coordinates of the points in which the following parametric equations will have horizontal or vertical tangents. x = t 3 - 3t        y = 3t 2 - 9 Solut

A company is taking bids on four construction jobs. Three Contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file. (A blank indicates n

Graph     ( x - 2) 2 /9+4(y + 2) 2  = 1 Solution It is an ellipse. The standard form of the ellipse is                                                         ( x - h