Transfer of heat

 Brief Intro:

1.Heat transfer from one point to another due to temperature difference.$\\$2.Its three mechanisms are Conduction, convection, and radiation.$\\$3.Conduction takes place in a material or between two materials in contact, convection depends on motion of$\\$molecules and so motion of mass from one region to another region of space and radiation is the$\\$heat transfer between the materials by the electromagnetic waves without any medium between them.

CM of Heat Transfer

$\text{Conduction:}$$\to$No actual movement of molecules takes place.$\\$$\to$Takes place mainly in solid and partially in liquid and gas.(reason > distance between molecules)$\\$$\to$Metals are good conductor of due to presence of free electrons in it.$\\$$\to$Steady state = No heat loss by leakage and rate of flow of heat is same throughout the conductor.$\\$$\to$Non-Steady state = Rate of heat flow varies from point to point. In this case heat loss takes place from body of conductor.$\\$

$\textbf{Temperature gradient:}\\$$\to$The rate of fall of temperature with distance in the direction of heat flow is called the temperature gradient.$\\$$\to$Temperature gradient=(θ1- θ2) / L (Where L is the distance between the point with temperature $θ_1$ and $θ_2 \\$

Heat Flow

$\text{Rate of flow of heat:}$$\to$The rate of flow of heat across a cube of side ‘l’ having face of area ‘A’ at different temperature $θ_1$ and $θ_2$ area depends on$\\$

1. Area of face of cube$\\$
2. Temperature difference of opposite faces$\\$
3. Distances of faces$\\$

Q/t =KA($θ_1$- $θ_2$)/l$\\$Where K is the thermal conductivity of matter of unit w/(mk) whose value depends on nature of conductor.$\\$Note: Silver has highest thermal conductivity.$\\$

$\textbf{Thermal resistance:}\\$$\to$Q/t =KA($θ_1$- $θ_2$)/l$\\$$\to$Q/t=( $θ_1$- $θ_2$)/(l/KA)$\\$Where Q/t = Rate of flow of heat is called heat current$\\$$θ_1$- $θ_2$= Temperature difference is equivalent to potential difference$\\$l/KA = R= is called thermal resistance which oppose the flow of heat current.$\\$

$\textbf{Combination of conductor:}\\$Series Combination=> $(Q/t)_1$=$(Q/t)_2$ => Req=$R_1$+$R_2 \\$Parallel Combination=>(Q/t)=$(Q/t)_1$+$(Q/t)_2 \\$1/Req =1/$R_1$ +1/$R_2 \\$Thermal conductivity of a good conductor by Searle`s Method:$\\$K= ms($θ_3$- $θ_4$-)/(A($θ_1$- $θ_2$)t)$\\$Where, k is thermal conductivity of the rod.$\\$

$\textbf{Application of Conduction:}\\$

1. Ice is packed in saw dust(reason: wood and air are bad conductor or heat)$\\$
2. Woolen clothes are warm because they have fine pores filled with air. (wool and air are bad conductor of heat)$\\$
3. Eskimos make double walled houses of the blocks of ice. ( air enclosed between the double wall is …..$\\$(good/bad) conductor of heat. Ans = bad)

Convection

$\textbf{Brief Discuss:}\\$$\to$Transfer of heat by actual motion of material.$\\$

$\to$Eg : Hot air furnace, the hot water heating system and flow of blood in the body.$\\$

$\to$Rate of transfer of heat in convection is directly proportion to the temperature difference between two parts of$\\$the convective fluid and to the surface area of the fluid exposed.$\\$

$\to$Heat is transmitted only vertically upward.$\\$

$\to$∆Q/t=hA∆θ$\\$

$\textbf{Application:}\\$

1. Room Ventilation (Warm air moves outside through the ventilators continuously keeping the room cool)
2. Trade winds (Convection current of air blows from north east towards the equator, which is called trade wind.)

Radiation

$\text{Brief Discuss:}$$\to$Medium is not needed.$\\$$\to$Heat transfer in the form of electromagnetic wave of speed 3*$10^8 \\$$\to$Fastest process$\\$$\to$Heat radiation lies in IR region$\\$$\to$Inverse square law in Heat Radiation$\\$I∝1/$R^2$$\\$Where I=intensity of heat radiation and R = Radius of sphere around the source$\\$

$\textbf{Note:}\\$$\to$When heat falls on a surface, a part of it is absorbed, a part of it is reflected and remaining part is transmitted.$\\$

$\to$Good reflectors are bad absorbers and vice versa$\\$

$\textbf{Black Body:}\\$$\to$Body that can absorb the entire heat radiation incident on it.$\\$$\to$It can also radiate all the wavelengths if heated at high temperature.$\\$$\to$No known body is perfectly blackbody.$\\$$\to$A surface coated with lamp black absorbs 96%to 98% of the incident radiation.$\\$$\to$A black body is perfect radiator.$\\$$\to$In ferry`s black body small opening acts as the black body radiator.$\\$

$\textbf{Emissive Power:}\\$$\to$Total energy of all wavelengths radiated per second per unit area of the body.$\\$$\to$Its SI unit is W/$m^2 \\$

$\textbf{Emissivity:} (e)\\$$\to$The ratio of energy radiated per unit area per unit time of a body and perfectly black body at same temperature.$\\$$\to$Its value is 1 for perfectly black body and less than 1 for any other bodies.$\\$$\to$e=Eԑ$\\$

$\textbf{Stefan-Boltzmann Law:}\\$$\to$Total amount of heat energy radiated per second per unit area of a perfectly black body is directly$\\$proportional to fourth power of its absolute temperature.$\\$E=σ$T^4 \\$Where E =Energy radiated per unit time per unit area$\\$Σ=5.67*$10^{-8}$ W/($m^2$ $K^4$)= Stefan`s Constant$\\$

If A is the surface area of the Body then$\\$E=σA$T^4$ or Power (P)=σ$T^4$$\\$

$\textbf{Thermal Enclosure:}\\$$\to$A body of temperature T is placed in an enclosure of$\\$Temperature $T_0$ then,$\\$1)If T>$T_0$, then rate of energy radiated$\\$(P)= σ($T^4$- $T_0^4$)$\\$2) If T<$T_0$, then rate of energy absorbed$\\$P= σ($T_0^4$ - $T^4$)$\\$

$\textbf{Prevost`s Theory of heat Exchange:}\\$$\to$According to this theory, everybody radiates heat radiation at all temperature.$\\$$\to$But when the body is at absolute zero temperature (-273˚C) it will not radiate any heat energy.$\\$

$\textbf{Wein`s displacement law:}\\$$\to$Can be used to determine the temperature of heavenly bodies.$\\$$\to$At maximum intensity of radiation for blackbody.$\\$$\to$λ.T=b where b=2.98*$10^{-3}$ m.k is called Wein`s constant$\\$∴ λ.T =λ'T'$\\$

$\textbf{Note:}\\$

1. If Body absorb radiation= Black$\\$
2. If body radiate more than surrounding=Bright$\\$
3. If body radiate same as surrounding=Invisible$\\$

$\textbf{Application of Radiation:}\\$1)White clothes are preferred in summer and dark colored clothes in winter. (Reason=White reflect and dark$\\$absorb radiations)$\\$

2)Polished reflectors are used in electric heaters to reflect maximum heat in the room.$\\$3)Hot water pipes and radiators used in room are painted black because they can radiate maximum amount of$\\$heat to the room.$\\$

$\to$Instruments for Detection and measurement of heat radiation:$\\$

1)Bolometer$\\$

2)Thermopile$\\$

$\textbf{Solar Constant:}(S)\\$$\to$Solar energy incident on unit area in unit time normally.$\\$$\to$It`s value is 1400 w/$m^2$ for surface of earth$\\$$\to$∴S=σ($R^2$/$r^2$ )$T^4 \\$Where R= Radius of sun$\\$r = Distance of earth from sun$\\$T=Temperature of sun

Points

$\text{Useful Information:}$$\to$Mercury though a liquid is heated by conduction and not by convection.$\\$$\to$It is the opening that acts as a black body in Ferry`s Black body.$\\$$\to$In a dark room a hot black body shines more than others.$\\$$\to$Radiation emitted from a perfectly black body does not depend on the nature of its material.$\\$$\to$Radiation is the fastest way of heat transfer.$\\$$\to$When a green glass is heated to high temperature it will glow with the red light.$\\$$\to$Birds often swell their feathers in winter because the air enclosed inside feather is bad conductor of heat.$\\$$\to$We cannot boil water inside an earth satellite by convection.$\\$$\to$Two thin blankets are warmer than a single blanket of double the thickness. (air trap inside the double blanket is$\\$bad conductor of heat)