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

$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=(Î¸1- Î¸2) / L (Where L is the distance between the point with temperature $Î¸_1$ and $Î¸_2 \\$

## Heat Flow

$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 $Î¸_1$ and $Î¸_2$ area depends on$\\$

- Area of face of cube$\\$
- Temperature difference of opposite faces$\\$
- Distances of faces$\\$

Q/t =KA($Î¸_1$- $Î¸_2$)/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$Q/t =KA($Î¸_1$- $Î¸_2$)/l$\\$$\to$Q/t=( $Î¸_1$- $Î¸_2$)/(l/KA)$\\$Where Q/t = Rate of flow of heat is called heat current$\\$$Î¸_1$- $Î¸_2$= 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($Î¸_3$- $Î¸_4$-)/(A($Î¸_1$- $Î¸_2$)t)$\\$Where, k is thermal conductivity of the rod.$\\$

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

- Ice is packed in saw dust(reason: wood and air are bad conductor or heat)$\\$
- Woolen clothes are warm because they have fine pores filled with air. (wool and air are bad conductor of heat)$\\$
- 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∆Î¸$\\$

$\textbf{Application:}\\$

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

## Radiation

$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$e=EÔ‘$\\$

$\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=Ïƒ$T^4 \\$Where E =Energy radiated per unit time per unit area$\\$Î£=5.67*$10^{-8}$ W/($m^2$ $K^4$)= Stefan`s Constant$\\$

If A is the surface area of the Body then$\\$E=ÏƒA$T^4$ or Power (P)=Ïƒ$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)= Ïƒ($T^4$- $T_0^4$)$\\$2) If T<$T_0$, then rate of energy absorbed$\\$P= Ïƒ($T_0^4$ - $T^4$)$\\$

$\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.