Foundations — Heat transfer — conduction (Fourier's law k), convection, radiation (Stefan-Boltzmann σT⁴)

1.7.6 · D1 · Physics › Thermodynamics › Heat transfer — conduction (Fourier's law k), convection, ra

Yeh page har woh symbol build karta hai jis par parent note depend karta hai, ek aisi reader ke liye shuru karke jisne kabhi ek bhi symbol nahi dekha. Har entry tumhe teen cheezein deta hai: seedha matlab → picture → topic ko yeh kyun chahiye. Upar se neeche padho; ladder ki har seedhi apne neeche wali par tikhi hai.

0. Heat aakhir hai kya? (ground floor)

Ek jar mein chhote balls (atoms) imagine karo jo kabhi ruk nahi rahe. Thande jar mein woh barely kaampte hain; garam jar mein woh hinsak tarike se hilte hain.

• Seedha matlab: $T$ atoms ki average jiggle energy measure karta hai.
• Picture: left jar = slow, chhote arrows; right jar = fast, bade arrows.
• Topic ko yeh kyun chahiye: yahan ki har single formula temperature ke difference se drive hoti hai. $T$ ke bina koi "hot" aur "cold" nahi, aur heat ke paas flow karne ki koi direction nahi.

1. Temperature measure karne ke do tarike: Celsius aur Kelvin

$T_{\text{K}}=T_{{}^{\circ }\text{C}}+273.15$

• Picture: ek vertical thermometer jisme do rulers side by side lage hain; tick marks ek line mein hain lekin har ek ka zero alag jagah par hai. Ticks ke beech ki spacing bilkul same hai.
• Topic ko yeh kyun chahiye — crucial subtlety: kyunki ticks same size ke hain, ek difference dono scales par same hota hai: $\Delta T=20^{\circ }\text{C}-0^{\circ }\text{C}=20\text{ K}.$ Lekin ek single value nahi hoti: $20^{\circ }\text{C}=293.15\text{ K}$, na ki $20$ K.

2. Rate of change: $\frac{dQ}{dt}$ ka matlab kya hai

Yeh tool kyun, bas "$Q$" kyun nahi? Ek wall total joules ki parwah nahi karti — woh flow speed ki parwah karti hai. "Har second kitne joules?" poochna exactly wahi hai jo ek rate answer karta hai, aur "per second, instant by instant" ke liye physics symbol derivative $\frac{d(\cdot )}{dt}$ hai.

• Picture: ek tap se nikalta paani. $Q$ bucket mein total litres hain; $\frac{dQ}{dt}$ yeh hai ki stream abhi is waqt kitni tezi se chal rahi hai.
• Is rate ka is topic mein ek naam hai: heat current $H$.

3. Temperature gradient $\frac{dT}{dx}$

• Picture: ek wall jo temperature ki ramp ki tarah draw ki gayi hai — left par hot face upar, right par cold face neeche. Us ramp ki slope hi $\frac{dT}{dx}$ hai. Steep ramp = bada gradient = heat ke liye strong push.
• Sign negative kyun hota hai: jab tum $+x$ direction mein (cold ki taraf) chalte ho, $T$ neeche jaata hai, isliye $\frac{dT}{dx}$ ek negative number hai. Heat opposite direction mein flow karti hai — $+x$ ki taraf — isliye Fourier's law mein $-$ hai taaki $H$ positive rahe.
• Topic ko yeh kyun chahiye: conduction raw temperatures se nahi, drop ki steepness se drive hoti hai. Gradient wohi steepness hai.

4. Area $A$ aur thickness $\Delta x$ — wall ki shape

• Picture: ek slab (ek brik). $A$ = woh flat front jise tum paint karoge; $\Delta x$ = brik front-to-back kitni gehri hai.
• Topic ko dono kyun chahiye: zyada chauda face ($A$) parallel mein zyada heat nikalne deta hai; zyada gehra brik ($\Delta x$) heat ko zyada travel karwata hai, use slow karta hai. Fourier's law mein yeh dono geometry ke knobs hain.

5. Material constants: $k$, $h$, $e$, $\sigma$

Transfer ka har mode apna "kitni aasaani se?" ek constant ke andar chhupata hai. Inse milo.

6. Power $P$ aur 4th power $T^4$

• Picture: chaar curves $T$, $T^2$, $T^3$, $T^4$ origin se upar udhte hue — $T^4$ baakiyon se bahut upar rocket karta hai. Wohi steepness hai kyun temperature mein thodi si rise radiated power mein badi uchhaal laati hai.
• Topic ko yeh kyun chahiye: radiation $P\propto T^4$ follow karta hai, isliye high temperature par yeh dominant loss channel ban jaata hai (ek filament, Sun) bhaale room temperature par tiny ho.

7. Thermal ↔ electrical analogy

Parent heat ko electricity par map karta hai. Dono pictures ko line up karo:

• Topic yeh kyun borrow karta hai: tum series/parallel resistor rules pehle se jaante ho; composite walls ke liye unhe reuse karna naya maths invent karne se bachata hai. High $\Delta T$ se "downhill flow" karne wali heat exactly high voltage se current flow jaisi hai.

Prerequisite map

Equipment checklist

Reveal karne se pehle har jawab zor se bolo.