Etoos Tips and Formulas Mode of Heat Transfer

MODE OF HEAT TRANSFER Heat Transfer 1. In conduction, heat is transferred from one point to another without the actual motion of heated particles. In the process of convection, the heated particles of matter actually move. In radiation, intervening medium is not affected and heat is transferred without any material medium. Conduction Heat Transfer due to Temperaturedifference Due to free electron or vibration motion of molecules Heat transfer in solid body (in mercury also) Slow process Convection Heat transfer due to density difference Radiation Heat transfer with out any medium Actual motion of particles Electromagnetic radiation Heat transfer in fluids (Liquid + gas) Slow process Fast process (3 × 108 m/sec) Irregular path Irregular path 2. All Straight line (like light) THERMAL CONDUCTION Electrical equivalent ? dQ dt Rate of heat flow dQ dt dQ dT = –KA dt dx Thermal resistance RH  Rods in series K eq  l l / K or Q KA (T1  T2 )  t l l KA Rods in parallel K eq  KA A THERMAL PROPERTIES OF MATTER 3. Growth of Ice on Ponds Time taken by ice to grow a thickness from x1 to x2 : t  ρL x22  x12 2 K   [K = thermal conductivity of ice,  = density of ice] 4. Radiation (a) Spectral, emissive, absorptive and transmittive power of a given body surface Due to incident radiations on the surface of a body following phenomena occur by which the radiation is divided into three parts. (a) Reflection (b) Absorption (c) Transmission (b) From energy conservation Qr Qa Qt Q = Q r + Q a + Qt    1  r+a+t=1 Q Q Q amount of incident radiation Q Qr Qa Reflective Coefficient r = , Absorptive Coefficient a = , Q Q Transmittive Coefficient t = r = 1 and a = 1 and t = 1 and a=0, r = 0, a = 0, t=0 t=0 r=0 Qt Q    amount of reflected radiation Qr amount of absorbed radiation Qa amount of transmitted radiation Q t Perfect reflector Ideal absorber (ideal black body) Perfect transmitter (daithermanons) Qr   1 00  % , Reflection power (r) =  Q  Qa   10 0  % Absorption power (a) =  Q  Qt   10 0  % Transmission power (t) =  Q   4. Stefan’s Boltzmann law : Radiated energy emitted by a perfect block body per unit area/sec E = T4 For a general body E = erT4 5. [where 0  e,  1] Prevost’s theory of heat exchange A body is simultaneously emitting radiations to its surrounding and absorbing radiations from the surroundings. If surrounding has temperature T0 then Enet = er (T4 – T04) 6. Kirchhoff’s law The ratio of emissive power to absorptive power is same for all surfaces at the same temperature and is equal to the emissive power of a perfectly black body at that temperature. e E E e = =  = E  e  a a A 1 a Therefore a good absorber is a good emitter. 7. Perfectly Black Body A body which absorbs all the radiations incident on it is called a perfectly black body. 8. Absorptive Power (a) Absorptive power of a surface is defined as the ratio of the radiant energy absorbed by it in a given time to the total radiant energy incident on it in the same time. For ideal black body, absorptive power = 1 9. Emissive power (e) For a given surface it is defined as the radiant energy emitted per second per u it area of the surface. 10. Newton’s law of cooling: If temperature difference is small Rate of cooling d  ( – 0) dt   = 0 + (1 – 0) e–kt [where k = constant] when a body cools from 1 to 2 in time ‘t’ in a surrounding of temperature 0 then 1   2 1 11.      k  1 2   0  [where k = constant]  2  Wien’s Displacement Law : Product of the wavelength m of most intense radiation emitted by a black body and absolute temperature of the black body is a constant m T = b = 2.89 × 10–3 mK = Wein’s constant  Area under e –  graph =  e d   e   T 0 4 THERMAL PROPERTIES OF MATTER 12. Solar constant The Sum emits radiant energy continuously in space of which an insignificant part reaches the Earth. the solar radiant energy received per unit area per unit time by a black surface held at right angles to the Sun’s rays and placed at the mean distance of the Earth (in the absence of atmosphere) is called solar constant. S where P 4 r 2  4 Rs2 T 4 4 r 2 2 R    s  T4  r  d R T A A' Rs = radius of sun r = average distance between sun and earth Note : S = 2 cal cm–2 min = 1.4 kWm–2 T = temperature of sun = 5800 K 13. Stainless steel cooking pans are preferred with extra copper bottom because thermal conductivity of copper is more than steel. 14. Two layers of cloth of same thickness because air (which is better insulator of heat) is trapped between them. 15. Animals curl into a bell when they feel very cold to reduce the surface area of the body. 16. Water cannot be boiled inside a satellite by convection because in weightlessness conditions, natural movement of heated fluid is not possible. 17. Metals have high thermal conductivity because metals have free electrons.