WHAT IS ACTUALLY "HEAT"?

Automobile engines, ovens, chemical reactions work due to heat. How to see , feel and understand the heat?

We know all the substances are made up of molecules. When the molecules are in motion(moving, vibrating, rotating etc.,) the substance is said to carry heat energy.

Take a hot tea in a cup and put a cold spoon in it. We know the spoon will be heated up. What happens? The molecules are in fast random motion in the hot tea. These molecules collide with the molecules of the spoon and set them in vibration. Now we say heat is transfered from tea to spoon.

As a speed of the molecules increases(kinetic energy), the heat content of the substance increases and we say the temperature increases.

Even at freezing point (at 0 degree c), the molecules really do not freeze but move at low speeds. When all the molecules come to stand still, we say the temperature is absolute zero or 0 degree kelvin. At 0 degree k: no movement , no heat, no temperature.

We know radiation or waves also cause heat. The radiation behaves like particles called photons. The movement of photon causes heat. In a microwave oven, the photons collide with water molecules in the food and the food is warmed up.

Imagine two balls. one is fast moving and other is slow moving. When the fast one hit the slow ball, the energy is transfered from first to the latter. The slow ball gains energy due to impact and moves fast. The fast ball slows down due to loss of energy. There is a high probability of transferring energy from fast ball to slow ball and not vice versa.

It is the same case in heat energy also. That is why the thermodynamic laws says it is impossible to transfer heat from a body of low temperature to a body of high temperature.

Heat passage also indicates time passage. As a time flows, heat also flows. So temperature is also a measure of time.

Next time, when you feel the hot water, remember that the fast moving water molecules dash against your skin with vengeance.

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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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