Tutor profile: Pradhumn M.
Subject: Basic Math
Define functions & Classify functions.
A function can be defined in various ways. Here I will explain a function with the help of various analogies. A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output is known as function. If we form a set of all the inputs then the set is known as domain and set of output is called Range, also the set of all possible output is called co-domain. Graphically, if we can draw even a single vertical line (perpendicular to x-axis) which intersects the curve in two or more points, then the curve does not represent a function. We can also think of a function as a kind of machine that produces an output value in its range whenever we feed it an input value x from its domain. Given that the machine should not produce more than one output for a single input. Functions can be classified in following ways: • Algebraic: 1. Polynomial 2. Rational 3. Irrational • Transcendental: 1. Exponential 2. Logarithmic 3. Trigonometric 4. Inverse Trigonometric • Conditional: 1. Modulus 2. Greatest Integer Function (G.I.F.) 3. Least Integer Function (L.I.F.) 4. Fractional 5. Signum
What is a chemical reaction? What are the factors which affects the rate of a chemical reaction? Explain in detail.
A chemical reaction is a process in which one or more substances, the reactants are converted to one or more products. In a chemical reaction, chemical changes take place. There may be changes in the physical state of the elements/compounds, reactants i.e. solid reactants may change to a liquid or gaseous state. A chemical reaction rearranges the constituent atoms of the reactants to create different substances as products. When a chemical reaction is performed in a lab. Following consideration has to be taken into mind: 1- The feasibility of chemical reaction. It means whether the chemical reaction is going to happen or not. Some times forward reaction is not feasible and the reaction takes place in backward direction only. The feasibility of a chemical reaction is described or decided by thermodynamics. In thermodynamics, we steady about free energy concept which decides the feasibility of a chemical reaction. If it is positive then the reaction will not take place, if it is negative then the reaction will take place. 2- Extent to which a reaction will proceed can be determined from chemical equilibrium. 3- Speed of a chemical reaction or rate of a chemical reaction i.e. how quick or slow a reaction achieves its equilibrium state. This is decided by the chemical kinetics of the chemical equation of the reaction. Factors affecting the rate of a chemical reaction : 1. Concentration 2. Temperature 3. Nature of reactants & products 4. Catalyst 5. pH of the solution 6. The dielectric constant of the medium 7. Radiations/light 8. Pressure 9. Electrical and magnetic field. 1. From the law of mass action, the rate is proportional to the concentration of reactants. So the rate of reaction decreases with the passage of time, since the concentration of reactants decreases. 2. Most of the chemical reactions are accelerated by an increase in temperature. It depends on whether the reaction is exothermic or endothermic. 3. Rate of a reaction depends upon the physical state of the reactants. Following is the order of the rate of reaction based on the physical state of the reactants : Gaseous > Liquid > Solid This is because collisions in homogeneous systems are more effective than heterogeneous system. As we decrease the particle size of the reactants, the reactants particle will be able to come closer and hence it will increase the rate of reaction. 4. Presence of a positive catalyst lower down the activation energy hence increases the rate of reaction. Presence of a negative catalyst increases the required activation energy hence decreases the rate of reaction. 5. Few reactions take place only in a particular medium. So it is important to note whether a reaction will require acidic, basic or neutral medium to take place. 6. More is the dielectric strength of the medium, greater will be the rate of chemical reaction. 7. Radiations are useful for photochemical reactions. E.g. Photosynthesis in plants take place in the presence of sunlight. 8. Pressure is important for gaseous reactions. For most of the reactions, increase in pressure increases the rate of reaction. 9. Electric and magnetic fields are rate determining factors if a reaction involves polar species.
Explain Critical Angle and Total Internal Reflection (TIR) in Geometrical optics?
Light Rays propagate through a medium. The medium should be transparent, not opaque. The speed of light is maximum in the vacuum which is equal to 299 792458 m/s. The speed of light depends upon the refractive index of the medium. The Refractive index tells us about the density of a medium. It tells us how much a medium is optically dense. If the refractive index of one medium is more as compare to another medium, it means the medium is optically denser as compared to the second medium, and hence the speed of light in the first medium is less as compared to the second medium. When a light ray passes from one medium to a second medium i.e. from air to water, water to air, air to vacuum, air to glass, glass to air, glass to water, water to glass, etc. then refraction of light takes place. It means the light rays bend from its initial path while entering the second medium. If light rays are coming from a rarer medium (a medium with lower refractive index) and entering a denser medium (a medium with higher refractive index) then the light rays will bend slightly towards the normal. If light rays are coming from a denser medium (a medium with higher refractive index) and entering a rarer medium (a medium with lower refractive index) then the light rays will bend slightly away from the normal. The extent to which light rays will bend depends on the ratio of refractive of the two mediums.
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