Tuesday, July 8, 2008

Laws and Theories - Revision Part 2

MaxWell's Speed Distribution Law

It is an equation giving the distribution of molecules in different speeds in a gas at a temperature.

If dN represents the number of molecules with speeds between v and v+dv then

dN = 4πN[m/2πkT]3/2v²e-mv²/2kTdv

where
dN represents the number of molecules with speeds between v and v+dv
N = total number of molecules in the gas
m = mass of a molecule
T = absolute temperature of the gas
v = velocity of the molecules

The speed vp at which dN/dv is maximum is called the most probable speed.
Its value is given by

vp = √(2kT/m)

(Topic: Kinetic theory of gases)


Avogadro's Law

Under similar conditions of temperature and pressure, equal volumes of all gases contain equal number of molecules.

(Basic concepts of chemistry)


Vectors

The sum of the resolved parts of two forces acting through a point along any direction is equal to the resolved part of the resultant of the two forces along that direction.

Explanation

If you find the resolved parts in some direction initially and then find their resultant, it will be equal to the resolved part of the resultant of the two forces in the same direction.

(Topic: Vectors)

Revision - Laws and Theories - 1

Laws of Thermodynamics

Zeroth law: If two bodies A and B are in thermal equilibrium and A and C are also in thermal equilibrium then B and C are also in thermal equilibrium.



First law of thermodynamics

∆U = ∆Q -∆W
Where
∆U = change in internal energy of a thermodynamic system
∆Q = Heat given to the system
∆W = work done by the system

Change in internal energy of a thermodynamic system is equal to the heat given to the system minus the work done by the system on surroundings or environment.

Second law of thermodynamics

Kelvin-Planck statement

It is not possible to design a heat engine which works in cyclic process and whose only result is to take heat from a body at a single temperature and convert it completely into mechanical work.


(Topic: Laws of Thermodynamics)



1. Law of conservation of mass

During any physical or chemical change, the total mass of the products is equal to the total mass of reactants.

2. Law of constant proportions

A pure chemical compound always contains same elements combined together in the same definite proportion by weight.

3. Law of multiple proportions

When two elements combine to form two or more than two compounds, the weights of one of the elements which combine with a fixed weight of the other, bear a simple whole number ratio.

4. Law of reciprocal proportions

When two different elements combine separately with the same weight of a third element, the ratio in which they do so will be the same or some simple multiple of the ratio in which they combine with each other.

5. Gay Lussac’s law of combing volumes

Under similar conditions of temperature and pressure, whenever gases react together, the volumes of the reacting gases as well as products (if gases) bear a simple whole number ratio.

Lagrange's Identity

(a × b)² = a²b² - (a.b)

a and b are vectors
a and b are magnitudes of a and b respectively.

Lagrange's identity is a relation between the cross product and the dot product.

(Topic: Vectors)