Foundations — Thermal expansion — linear, area, volumetric

1.7.7 · D1 · Physics › Thermodynamics › Thermal expansion — linear, area, volumetric

Yeh page toolbox hai. Pehle hum parent note Thermal expansion par koi bhi formula use kar sakein, hume har symbol earn karna hoga — plain words mein uska matlab bolna hoga, uske peeche ka picture draw karna hoga, aur explain karna hoga ki topic ko uski zaroorat kyun hai. Yahan kuch bhi assume nahi kiya gaya ki tumne pehle yeh notation dekha hai.

0 · "Temperature" aur "heat" ka matlab yahan kya hai

Do thermometers ka picture socho: ek start mein (thanda), ek end mein (garam). $\Delta T$ unki readings ke beech ka gap hai — bas itna hi.

Topic ko $\Delta T$ kyun chahiye: expansion heating se drive hoti hai, toh sabse pehli cheez jo hum measure karte hain woh hai object kitna zyada garam hua.

1 · Length, aur letter $L$

Ek rod ka picture jise do baar draw kiya gaya hai: ek chhota thanda bar labeled $L_0$, aur us ke bilkul neeche ek bahut thoda sa lamba garam bar labeled $L$.

Topic ko iski zaroorat kyun hai: jo kuch bhi hum build karte hain woh in do lengths ke difference ke baare mein hai.

2 · Length mein change, $\Delta L$

Figure mein, $\Delta L$ woh chhota overhang hai jo garam bar ka thande bar ke end se aage nikla hua hai.

3 · BIG idea: fractional change $\frac{\Delta L}{L}$

Yeh poore topic ka sabse important notation hai.

Picture: ek lamba bar aur ek chhota bar, dono shaded hain taaki har ek ka same fraction "growth" ke roop mein colored ho. Colored pieces absolute size mein alag lagte hain lekin poore ka same slice hain.

4 · Coefficients $\alpha$, $\beta$, $\gamma$

Ab woh Greek letters jo material ki expansion rate ko name karte hain.

"Per degree" isliye units $K^{-1}$ hain: tum ek plain fraction paate ho har 1 K rise ke liye, toh $\frac{\Delta L}{L}=\alpha \Delta T\Rightarrow \alpha =\frac{1}{\Delta T}\cdot \frac{\Delta L}{L}.$

Topic ko inki zaroorat kyun hai: $\alpha$, $\beta$, $\gamma$ woh numbers hain jo tum table mein lookup karte ho steel, glass, copper ke liye — poori baat yeh hai ki inhe formula mein plug karo aur growth predict karo.

5 · Powers: $L^2$ ka matlab area hai, $L^3$ ka matlab volume

Sheets aur blocks ke baare mein baat karne se pehle hume sure hona chahiye ki ek chhoti raised number ka matlab kya hai.

Ek square ka picture jise $L\times L$ chhote unit squares se tile kiya gaya hai (woh count $L^2$ hai), aur ek cube jo $L\times L\times L$ chhote unit cubes se stack kiya gaya hai (woh count $L^3$ hai).

6 · Symbol $A_0(1+\alpha \Delta T{)}^2$ padhna

Hume algebra literacy ka ek aur piece chahiye: ek bracket ko square karna.

Yahan $x$ chhoti quantity $\alpha \Delta T$ ke liye stand karta hai. $x$ ke aage $2$ (square ke liye) aur $3$ (cube ke liye) exactly wahi hain jahan se $\beta =2\alpha$ aur $\gamma =3\alpha$ aate hain.

7 · Hum "small terms drop" kyun kar sakte hain (symbol $\approx$)

Isi wajah se exact law $L=L_0{e}^{\alpha \Delta T}$ (jahan $e\approx 2.718$ hai, natural exponential — woh number jo apne current size se grow karta hai) $e^x\approx 1+x$ ke through simplify hokar everyday form mein aa jaata hai: $L\approx L_0(1+\alpha \Delta T).$

Is page ke liye tumhe calculus ki zaroorat nahi — bas trust karo ki bahut chhota $x$ $e^x$ aur $1+x$ ko almost identical bana deta hai, jo figure dikhata hai.

Prerequisite map

Equipment checklist

Khud ko test karo — answer karne ke baad hi reveal karo.

Connections

• Thermal expansion — linear, area, volumetric — parent topic jinhe yeh tools unlock karte hain.
• Kinetic theory of gases — jahan "jiggling atoms" ko quantitative banaya jaata hai.
• Interatomic potential energy curve — kyun average spacing bahar ki taraf drift karti hai.
• Gas laws — woh ek jagah jahan tumhe absolute $T$ use karni hi padegi, sirf $\Delta T$ nahi.