72
Graphical Representation
In a plot such as that in Figure 6-5, one can eliminate the extra labor of
converting all the pressure values to the corresponding logarithms by using
semilog graph paper, which has a logarithmic scale in one direction and the
usual linear scale in the other Semilog paper is available in one-cycle, twocycle, or three-cycle forms (and so on), with each cycle able to handle a 10-fold
spread of data For example, one-cycle paper can handle data from 0 1 to 1 0,
or 1 0 to 10 0, or 10
4 to 10', and so on Two-cycle paper can handle data from
10~
4 to 10~-, or 0 1 to 10, or 10 to 1000, and so on Always choose the paper with
the smallest number of cycles that will do the job, in order to have the largest
possible graph on the paper The use of this kind of paper is illustrated in the
following problem
PROBLEM:
Calculate the heat of vaporization of water, using the data of Table 11-1 in a
semilog plot
SOLUTION:
It still is necessary to convert the Celsius temperature values to reciprocal degrees
Kelvin, as in the previous problem, but the pressure values can be used directly,
as shown in Figure 6-6
At this point, take great care in calculating the slope of the line because al
though a logarithmic tcale was used, the values shown along the ordmate are not
logarithmic values In calculating the slope, therefore, select two convenient
points on the line, but convert the two pressure values selected into their
logarithms before making the calculations For example, in Figure 6-6 when 1/7 x
10' is 2 85, the value of P is 323, and log P is 2 509 Similarly when 1/7 x 10
! is
3 00, P is 150, and log P is 2 176 Thus the slope is given by
2176-2509 = _ 222X1Q .
0 00300 - 0 00285
As before,
A//, ~-(m)(2 303)(fl) - -(-2 22 x 10
! )(2 303)(1 987)
- + 1 02 x 10* cal/mole
THE METHOD OF LEAST SQUARES
"Draw a smooth curve that best represents all the points, such a curve may not
necessarily pass through any of the points " This is the sixth guideline given for
curve construction on p 65. In all of the figures of this chapter, we have assumed that this has indeed been done Nevertheless, curve drawing is a rather
subjective process, prone to many abuses, unless some objective rules are
Graphical Representation
In a plot such as that in Figure 6-5, one can eliminate the extra labor of
converting all the pressure values to the corresponding logarithms by using
semilog graph paper, which has a logarithmic scale in one direction and the
usual linear scale in the other Semilog paper is available in one-cycle, twocycle, or three-cycle forms (and so on), with each cycle able to handle a 10-fold
spread of data For example, one-cycle paper can handle data from 0 1 to 1 0,
or 1 0 to 10 0, or 10
4 to 10', and so on Two-cycle paper can handle data from
10~
4 to 10~-, or 0 1 to 10, or 10 to 1000, and so on Always choose the paper with
the smallest number of cycles that will do the job, in order to have the largest
possible graph on the paper The use of this kind of paper is illustrated in the
following problem
PROBLEM:
Calculate the heat of vaporization of water, using the data of Table 11-1 in a
semilog plot
SOLUTION:
It still is necessary to convert the Celsius temperature values to reciprocal degrees
Kelvin, as in the previous problem, but the pressure values can be used directly,
as shown in Figure 6-6
At this point, take great care in calculating the slope of the line because al
though a logarithmic tcale was used, the values shown along the ordmate are not
logarithmic values In calculating the slope, therefore, select two convenient
points on the line, but convert the two pressure values selected into their
logarithms before making the calculations For example, in Figure 6-6 when 1/7 x
10' is 2 85, the value of P is 323, and log P is 2 509 Similarly when 1/7 x 10
! is
3 00, P is 150, and log P is 2 176 Thus the slope is given by
2176-2509 = _ 222X1Q .
0 00300 - 0 00285
As before,
A//, ~-(m)(2 303)(fl) - -(-2 22 x 10
! )(2 303)(1 987)
- + 1 02 x 10* cal/mole
THE METHOD OF LEAST SQUARES
"Draw a smooth curve that best represents all the points, such a curve may not
necessarily pass through any of the points " This is the sixth guideline given for
curve construction on p 65. In all of the figures of this chapter, we have assumed that this has indeed been done Nevertheless, curve drawing is a rather
subjective process, prone to many abuses, unless some objective rules are