Indian Deities Worshipped in Japan

University of Cambridge: The interactive Ellingham diagram

Thermodynamics:
The interactive Ellingham diagram

Here we shall go through the basic thermodynamics that lies behind use of the Ellingham diagram. First, we will establish the link between the thermodynamics of a reaction and its chemistry.

The Gibbs free energy, G, of a system can be described as the energy in the system available to do work. It is one of the most useful state functions in thermodynamics as it considers only variables contained within the system, at constant temperature and pressure.

It is defined as:

        (1)

Here, T is the temperature of the system and S is the entropy, or disorder, of the system. H is the enthalpy of the system, defined as;

       (2)

Where U is the internal energy, p is the pressure and v is the volume.

To see how the free energy changes when the system is changed by a small amount, we can differentiate the above functions:

       (3)

and;

       (4)

From the first law,

       (5)

and from the second law,

,        (6)

we see that,

       (7)

since work, .

The above equation shows that if the temperature and pressure are kept constant, we see that the free energy does not change. This means that the Gibbs free energy of a system is unique at each temperature and pressure.

At a constant temperature dT = 0 and so

       (8)

We can find G for the system by integration. To do this we need the system’s equation of state, to give a relationship between v and p.

We will consider an ideal gas. For one mole of an ideal gas the equation of state is;

,       (9)

so (8) becomes

.        (10)

Integrating:

       (11)

This we can express as

       (12)

We define G° to be the standard free energy at the standard pressure, p°. These standard values are nothing more than lower integration constants, but using them is very useful, as we shall see. They are a consequence of the fact that one can only describe energy changes absolutely – there is no absolute energy scale, so the energy value we give to a system is arbitrary. 

Chemical Reactions:

We will now see why studying the free energy of a system is useful in determining its behaviour.

The free energy change, ΔG, of a chemical reaction is the difference in free energy between the products of the reaction and the reactants. If the free energy of the products is less than the free energy of the reactants there will be a driving force for the reaction to occur.

For the reaction

,

the free energy change,

                (13)

    (14)

if the standard states . We see that the free energy change of a reaction is determined by the relative quantities of reactants and products.

The Equilibrium Constant:

A chemical reaction will occur if the total free energy of the products is less than the total free energy of the reactants. (ie. The free energy change for the reaction is negative.) If the system containing the reactants and products is closed (if there is no input of reactants, for example), the concentration of reactants will decrease and the concentration of products will increase as the reaction proceeds. This will alter the state of the system and therefore alter the free energy change for the reaction (see equation 14, above).

The reaction will continue if the free energy change remains negative. Hence, the system proceeds down a free energy gradient with respect to composition and this gradient provides the driving force for the reaction to proceed. The system alters the quantities of reactants and products in response to the driving force until a minimum in free energy is reached and the gradient is zero. This is a point of equilibrium.

At equilibrium the free energy change for the reaction is equal to zero:

Therefore

     (15)

For the composition at equilibrium, the quotient is equal to K_P - the equilibrium constant for the reaction at constant pressure. We see that the equilibrium composition of the system is defined by the standard free energy change, ΔG°. Equation 15 provides a link between the thermodynamics of a reaction and its chemistry. ΔG° for a reaction is hence a very useful value to know.

Partial pressure of reacting gas:

Using equations (15) we can see that the equilibrium constant is related to the partial pressures of reacting gases:

for the reaction . (Remember that these pressures must be related to a standard state.)

For a metal oxidation reaction ,

2M _(s) + O_{2 (g)} = 2MO _(s) ,

the equilibrium constant has the form

.

Click here for a more detailed discussion of the equilibrium constant.

We can therefore find the equilibrium partial pressure of oxygen at a particular temperature from the value of ΔG°:

.

The equilibrium partial pressure of oxygen is the pressure at which the driving force for the reaction is zero. From equation 14 we see that if the partial pressure of oxygen is greater than this value, the free energy change for the reaction is negative and there is a driving force for the reaction to take place. Metal will be oxidised, and the partial pressure of oxygen will drop until it reaches equilibrium. This is effect described by Le Chatelier’s principle.

If the partial pressure of oxygen is below the equilibrium value, oxidation is avoided. (In fact, the metal oxide will disassociate to form metal plus oxygen gas-this is because there is a driving force for the reaction to proceed backward. For this reason the equilibrium partial pressure is often known as the dissociation pressure.)

Reading pO2 from the Ellingham diagram

MKS, CGS AND SI SYSTEMS

MKS is the system of units based on measuring lengths in meters, mass in kilograms, and time in seconds. MKS is generally used in engineering and beginning physics, where the so-called cgs system (based on the centimeter, gram, and second) is commonly used in theoretic physics. The most familiar units of electricity and magnetism (ohm, farad, coulomb, etc.) are MKS units.
 
CGS is the system of units based on measuring lengths in centimeters, mass in grams, and time in seconds. It is a metric system, although not the flavor of the metric system used most commonly. It was introduced by the British Association for the Advancement of Science in 1874, and was immediately adopted by many working scientists.

There are several flavors of the cgs system: "cgs electrostatic," "cgs electromagnetic," and "cgs Gaussian." None of these are part of the SI system, except for units such as the centimeter defined in both systems (Taylor 1995, p. 11). The cgs Gaussian system is nonetheless commonly used in theoretical physics, while the MKS system (based on the meter, kilogram, and second) is commonly used in engineering and physics instruction.

unit	symbol	MKS (abbrev.)	cgs (abbrev.)
acceleration	a	m s	Gal
capacitance	C	Farad (F)	cm
charge	q	Coulomb (C)	esu
current	I	Ampere (A)	esu s-1
electric field	E	V m-1	statvolt cm-1
electric potential	V,	Volt (V)	statvolt
energy, work	E, W	Joule (J)	erg
force	F	Newton (N)	dyne
inductance	L	Henry (H)	cm-1 s
length	l, d	meter (m)	centimeter (cm)
magnetic field	B	Tesla (T)	Gauss (G)
magnetic flux		Weber (w)	Gauss cm
mass	m	kilogram (kg)	gram (g)
momentum	p	kg m s-1	g cm s-1
power	P	Watt (W)	erg s-1
pressure	P	Pascal (Pa)	bar
resistance	R	Ohm ()	cm-1 s
temperature	T	Kelvin (K)	Kelvin (K)
time	t	second (s)	second (s)
velocity	v	m s-1	cm s-1

"SI" stands for "System International" and is the set of physical units agreed upon by international convention. The SI units are sometimes also known as MKS units, where MKS stands for "meter, kilogram, and second." In 1939, the CCE recommended the adoption of a system of units based on the meter, kilogram, second, and ampere. This proposal was approved by the Comité International des Poids et Mesures (CIPM) in 1946. Following an international inquiry by the Bureau International des Poids et Mesures (BIPM), which began in 1948, in 1954 the 10th Conférence Générale des Poids et Mesures (CGPM) approved the introduction of the ampere, kelvin, and candela as base units for electric current, thermodynamic temperature, and luminous intensity, respectively. However, the ampere is scheduled to be phased out as a base unit in the near future in favor of the ohm, which can be measured extremely accurately using the quantum Hall effect. In turn, the volt will probably replace the ohm further in the future when measurements using Josephson junctions increase in precision.

The name International System of Units (SI) was given to the system by the 11th CGPM in 1960. At the 14th CGPM in 1971, the current version of the SI was completed by adding the mole as base unit for amount of substance, bringing the total number of base units to seven. The seven fundamental units are summarized in the following table.

physical quantity	symbol	unit abbreviation	unit name
length	l	m	meter
mass	m	kg	kilogram
time	t	s	second
current	I	A	Ampere
temperature	T	K	Kelvin
luminous intensity		cd	candela
amount of substance	n	mol	mole

The derived SI units consist of combinations of the seven base units, and are summarized in the following table.

quantity	symbol	SI symbol	SI unit
area	A		square meter
volume	V		cubic meter
plane angle		rad	radian
solid angle		sterrad	steradian
frequency	f	Hz	Hertz
velocity	v		meters per second
acceleration	a		meters per second squared
force	F	N	Newton
pressure	P or p	Pa	Pascal
power	P	W	Watt
energy	E	J	Joule
voltage	V	V	Volt
resistance	R		Ohm
conductance	G	S	Siemens
charge	Q	C	Coulomb
capacitance	C	F	Farad
magnetic flux		Wb	Weber
magnetic flux density	B	T	Tesla
inductance	L	H	Henry
luminous flux	F	lm	lumen
illumination	E	lx	lux
activity	A	Bq	Becquerel
energy dose		Gy	Gray
equivalent dose		Sv	Sievert

In 1960, the 11th CGPM adopted a first series of prefixes and symbols of prefixes to form the names and symbols of decimal multiples and submultiples of SI units. Over the years, the list has been extended as summarized in the following table.

factor	prefix	symbol
1024	yotta-	Y
1021	zetta-	Z
1018	exa-	E
1015	peta-	P
1012	tera-	T
109	giga-	G
106	mega-	M
103	kilo-	k
102	hecto-	h
101	deca-	da
	deci-	d
	centi-	c
	milli-	m
	micro-
	nano-	n
	pico-	p
	femto-	f
	atto-	a
	zepto-	z
	yocto-	y

PHYSICAL FEATURES OF INDIA:MAJOR PHYSIOGRAPHIC DIVISIONS

The physical features of India can be grouped under the following physiographic divisions:
(1) The Himalayan Mountains
(2) The Northern Plains
(3) The Peninsular Plateau
(4) The Indian Desert
(5) The Coastal Plains
(6) The Islands
The Himalayan Mountains:

The Himalayas, geologically young and structurally fold mountains stretch over the northern borders of India. These mountain ranges run in a west-east direction from the Indus to the Brahmaputra. The Himalayas represent the loftiest and one of the most rugged mountain barriers of the world. They
form an arc, which covers a distance of about 2,400 Km. Their width varies from 400 Km in Kashmir to 150 Km in Arunachal Pradesh. The altitudinal variations are greater in the eastern half than those in the western half. The Himalaya consists of three parallel ranges in its longitudinal extent. A number of valleys lie between these ranges. The northern most range is known as the Great or Inner Himalayas or the ‘Himadri’.It is the most continuous range consisting of the loftiest peaks with an average height of 6,000 metres. It contains all the prominent Himalayan peaks.
The folds of Great Himalayas are asymmetrical in nature. The core of this part of Himalayas is composed of granite. It is perennially snow bound, and a number of glaciers descend from this range.
The range lying to the south of the Himadri forms the most rugged mountain system and is known as Himachal or lesser Himalaya. The ranges are mainly composed of highly compressed and altered rocks. The altitude varies between 3,700 and 4,500 metres and the average width is of 50 Km. While the Pir Panjal range forms the longest and the most important range, the Dhaula Dhar and the
Mahabharat ranges are also prominent ones.