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Basic Science & Engineering INDIA RRB ALP & Technicians Recruitment 2018 for Railway ALP CBT2 Basic Science Heat & Temperature
Different bodies (i) If a = t = 0 and r-1 body is perfect reflector (i) If r = t = 0 and a = 1 body is perfectly black body (ii) Ifa and t -1-> body is perfect transmitter (iv) If t :-0 r + a l or -1-r, i.e., good reflectors are bad absorbers. Perfectly Black Body A black body is defined as one that will completely absorb all the radiations of whatever wavelength which falls on it. For perfectly black body, a-1 Properties ofperfectly black body: (i) A perfectly black body absorbs all the radiant heat incident (ii) A perfectly black body does not reflect or transmit the radiant (iii) The coefficient ofemission of a perfectly black body is l. It (iv) A perfectly black body does not exist in nature. upon it. (i.e. a-1) heat incident upon it. (i.e. t 0, r is very good emitter of heat. O)
For practical purposes lamp black is treated as a perfectly black body as its coefficient-of absorption is nearly 0.98. Wien's Displacement Law According to Wien's displacement law Here, constant b is known as Wien's constant Stefan's Law of Heat Radiation The energy (Emax) emitted corresponding to the wavelength of maximum emission (m) increases with the fifth power of the absolute temperature of the black body. It is known as Wien's fifth power law
Solar Constant 2 ER Solar constant, S-_ But, E-0T4 (according to Stefan's law 2 or 4 2 2 Here, S-1400 Wm-2,R-6.96 x 108 m,r- 1.496 x 1011 m = 5.68 1 0-8 SI unit On substituting these values above, we get T, the surface temperature ofthe Sun. It comes out to be equal to 5791 K. In this way, the surface temperature of Sun has been estimated.
Kirchhoffs Law of Heat Radiation At any given temperature and for radiations of the same wavelength the ratio of the ernissive power (es) to the absorptive power (aj) is the same for all substances and is equal to the emissive power of a perfectly black body (E 1.e.,-= const.= E Also, absorptive power of a body is equal to its emissivity. Stefan Boltzmann Law of Radiation According to Stefan Boltzmann law, the quantity of heat energy radiated in one second per unit area of a perfectly black body is directly proportional to the fourth power of its absolute temperature. E, Tor
where is a universal constant known as Stefan-Boltzmann constant and T is its temperature on absolute scale. The measured value of is 5.67x 10-8 W/m2-K4 or 5.67x 10-5 erg/cm?sKa The eqn. Eb- T4 is called the Stefan-Boltzmann law. . Total energy radiated by the surface of a body in time t Cooling ofa body by radiation Consider a perfectly black body of absolute temperature T is surrounded by another black body at absolute temperature To- Let, the surface area of the perfectly black body-A The rate of loss of heat of the perfectly black body dQ Let, the emissivity of an ordinary body- E The rate of loss of heat of the ordinary body de- A e [T4-T- cal/sec Rate of fall oftemperature dt msJ
Newton's law of cooling The rate of cooling of a body (rate of loss of heat) is directly proportional to the excess of temperature of the bocy over the surToundings, provided that this excess is small and loses of heat byy radiation only. If0 and o are the temperatures of the body and its surroundings respectively, then according to Newton's law of cooling, dQ dt Rate ofloss of heat,- oc ( _ 0) The negative sign indicates that the amount of heat is decreasing with time dt where k is the constant of proportionality. Rate offall of temperature dt (m and s are constant.) dt Thus, Newton's law of cooling can also be stated as The rate of fall oftemperature ofa body is directly proportional to excess of temperature of the body over the surroundings. provided that excess is small.
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