WHY DOES NOT A STORM ARRANGE EVERYTHING IN THE STREET NEATLY?

We are going to look at the second law of thermodynamics at another angle.

Ice melts to water; coffee cools down to room temperature; when a balloon is pierced, air rushes out; glass cup falls down, broken into pieces; acid and base combines to form salt and water. The above actions and reactions takes place spontaneously. Our common sense and intuition vouch for it.

Why the reverse should not happen? Why not water turn into ice; why not air thrust itself into balloon; why not broken pieces join to form a cup; why particular direction for actions? The second law answers.
An action will take place only when disorder or entropy increases in the surroundings or universe. In short, change in entropy should be positive.

When the coffee looses heat, the room is slightly warmed up. The air from balloon rushes out and disturb the order in surroundings. The broken pieces have more disorder than a full cup. That is the reason for the direction of happenings.

Why disorder? Because of probability, when you shuffle a deck of cards, there is a strong probability that it will go into disorderly arrangement. It will never go into 1....10,j,q,k arrangement even though it is possible.

Instead of measuring the change in entropy in the universe, there is short cut called
Gibbs free energy = internal energy- temperature* entropy

If the entropy is positive, and if the Gibbs energy is negative, an action will happen spontaneously without any aids. If not, only forced (heating, pressuring etc,) actions will take place.
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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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