Question

1. Make a plot of Specific heat versus Atomic number. Fit it to a Power-Law.

Alkali metal	Atomic number	Atomic weight	Specific heat (J/g/°K)
Lithium	3	6.941	3.582
Sodium	11	22.99	1.228
Potassium	19	38.098	0.757
Rubidium	37	86.468	0.363
Cesium	55	132.905	0.242
Francium	87	223	—

a. What is the power (of your Power-Law trendline)? What is the coefficient?

b. If you were to use the formula to predict a specific heat of Francium, what is the predicted specific heat?

Answer 1

Question is related to Dulong and Petit law. Using data we plot a graph between Specific heat and Atomic number.

Atomic Number is represented by letter Z . Specific heat is represented by letter C. The graph is given below.

a) To find power law

As the graph between specific heat and atomic number is not linear (Rectangular hyperbola). It is difficult to find a relation between them. So we plot a graph between ln C Vs ln Z. The graph is given below.

Here, we get a approximately a straight line. A straight is generally represented by the equation

y = mx + c

where m = slope of line

c = y- intercept

By taking any two arbitary points from line, we can find slope m. Let two points be (x1,y1) and (x2,y2)

If we extent the straight line, It intersect y-axis at one point. The ordinate of y-axis is called y-intercept.

From graph we get,

m = -0.93

c = 2.36

so equation of straight line is

is Power law

Co-efficent of law = 10.59

Power of law = -0.93

b) Specific Heat C is related to atomic Z by power law as :

For Francium Z = 87

C = 0.166 J/g/K is Specific heat of Francium.