Heat engines — efficiency η = 1 − Q_C - Q_H: Foundations

1.7.19 · D1 · Physics › Thermodynamics › Heat engines — efficiency η = 1 − Q_C - Q_H

Is page par parent topic ka har symbol bilkul zero se build kiya gaya hai, ek aisi order mein jahan har idea apne pehle wale idea par tikaa hua hai. Koi bhi cheez use nahi hoti jab tak woh draw na ho jaaye.

1. Energy — woh cheez jo idhar-udhar move hoti hai

Topic ko yeh kyun chahiye: Heat engine mein har cheez — andar aane wali heat, bahar jaane wala work, dump ki gayi heat — sab energy hi hai, bas alag-alag roop mein. Poori efficiency formula ek badi statement hai ki coins kahan gayi.

2. Heat $Q$ — energy jo temperature difference ki wajah se move karti hai

Letter $Q$ sirf "is flowing energy ki ek matra" ka naam-tag hai. Jab hum subscript likhte hain jaise $Q_{H}$ , toh chhota sa $H$ batata hai ki kaunsi heat hum mean kar rahe hain — bas itna hi.

Figure — Heat engines — efficiency η = 1 − Q_C - Q_H

Kyunki heat "energy on the move" hai, hum is chapter mein $Q$ ko hamesha ek magnitude (positive amount) ke roop mein lete hain aur direction batane ke liye words use karte hain ("in" / "out"). Toh $Q_{H} > 0$ aur $Q_{C} > 0$ ; direction subscript mein hai, minus sign mein nahi.

3. Temperature $T$ aur do reservoirs $T_{H}$ , $T_{C}$

Topic ko yeh kyun chahiye: engine ko baar-baar chalne ke liye ek fixed hot side aur ek fixed cold side chahiye. Subscripts heats se match karte hain: $Q_{H}$ reservoir se aata hai jo $T_{H}$ par hai, $Q_{C}$ reservoir mein jaata hai jo $T_{C}$ par hai.

Kelvin kyun, Celsius kyun nahi? Carnot formula mein do temperatures ka ratio hota hai, $T_{C} / T_{H}$ . Ratio tabhi physical sense deta hai jab $0$ ka matlab "bilkul koi temperature nahi" ho. Celsius scale par $0° C$ sirf "paani ka freezing point" hai — ek arbitrary jagah — toh wahan ratios meaningless hain. Kelvin ka zero sachcha zero hai, isliye ratios sahi behave karte hain.

4. Work $W$ — organised energy jo dhakka deti hai

Topic ko yeh kyun chahiye: work useful output hai — woh cheez jiske liye engine exist karta hai. Heat messy, disorganised energy hai; work neat, usable energy hai (ek ghoomta hua shaft, chalti hui car). $Q$ ko $W$ mein badalna engine ka poora kaam hai.

Figure mein poora flow dikhta hai: $Q_{H}$ hot side (upar) se enter karta hai, engine (red box) work ke roop mein $W$ drain kar leta hai, aur bacha hua $Q_{C}$ cold side mein neeche gir jaata hai. Picture ko ek accountant ki tarah padho: jo bhi upar se andar aata hai woh bahar jaana chahiye — kuch work ke roop mein side se, baaki heat ke roop mein neeche se.

5. Internal energy $U$ aur state functions

Topic ko yeh kyun chahiye: engine ek cycle mein chalta hai — woh har chakkar mein apni starting state par wapas aata hai. Kyunki $U$ ek state function hai, ek poore loop mein $Δ U = 0$ hota hai. Yeh ek akela fact hi humein kehne deta hai ki saari net heat kaam ban gayi.

6. Delta symbol $Δ$ aur "cycle"

Yeh dono milaao: ek cycle mein, kyunki gas wahan wapas aati hai jahan se shuru hui thi, $Δ U_{cycle} = U_{end} - U_{start} = 0$ . Yeh parent ke derivation mein keystone step hai.

7. First Law — accounting rule

Topic ko yeh kyun chahiye: is law ko ek cycle par apply karo jahan $Δ U = 0$ ho, $Q_{net} = Q_{H} - Q_{C}$ plug in karo, aur tumhe turant mil jaata hai $W = Q_{H} - Q_{C}$ — engine ka dil. Upar ke har symbol ki zaroorat thi taaki yeh ek line padhne laayak bane.

8. Efficiency $η$ aur ratio ki idea

$η$ ki units kyun nahi hoti: yeh joules divided by joules hai, toh units cancel ho jaati hain. Isliye efficiency ek pure number hai (ya percentage). Kyunki $W = Q_{H} - Q_{C}$ hai, $Q_{H}$ se divide karne par definition famous $η = 1 - Q_{C} / Q_{H}$ ban jaati hai.

Figure mein bar $Q_{H}$ ko do pieces mein split karta hai: useful slice $W$ (red) aur wasted slice $Q_{C}$ (black). Efficiency bas bar ka woh fraction hai jo red hai. Ab tum instantly dekh sakte ho kyun $η$ kabhi $1$ tak nahi pahunch sakta: black slice $Q_{C}$ shrink ho sakta hai lekin poori tarah kabhi disappear nahi ho sakta.

Yeh topic ko kaise feed karte hain

Equipment checklist

Right side cover karo aur khud ko test karo — tum parent note ke liye ready ho jab har line easy lage.

Energy, heat, aur work ki units kya hain?

Joule,

J

— yeh saari same tarah ki quantity hain (energy).

Q_{H}

mein subscript tumhe kya batata hai?

Kaunsi heat hai — yahan, hot reservoir ke saath

T_{H}

par exchange ki gayi heat.

Heat khud-ba-khud kis direction mein flow karti hai?

Hot se cold ki taraf, kabhi ulti nahi (ek-taraf, jaise paani neeche bahta hai).

Reservoir kya hota hai?

Ek aisi body jo itni badi ho ki heat dene ya lene par bhi uski temperature fixed rahe.

Carnot formula mein kelvin kyun use karna chahiye, Celsius kyun nahi?

Temperature ke ratios tabhi sense dete hain jab ek sachcha zero ho; kelvin ka zero real hai, Celsius ka arbitrary hai.

Work aur heat mein kya fark hai?

Work ordered, usable energy hai (distance par push); heat disordered energy hai jo temperature difference ki wajah se flow karti hai.

State function kya hota hai, aur yahan kaunsi quantity ek hai?

Ek quantity jo sirf current state par depend kare, path par nahi — internal energy

U

Cycle mein

Δ U = 0

kyun hota hai?

Gas apni start state par wapas aati hai, aur

U

(ek state function) wahan same hoti hai.

First Law symbols mein batao.

Δ U = Q_{net} - W

η

ek phrase mein kya mean karta hai, aur uski units kya hain?

Useful work out divided by heat paid in; yeh ek pure number hai (unitless).

Connections

First Law of Thermodynamics — yahan build ki gayi energy-accounting rule.
Second Law of Thermodynamics — kyun wasted slice $Q_{C}$ kabhi vanish nahi ho sakti.
Carnot Cycle — is page se kelvin ki idea chahiye.
Entropy — deeper reason ki heat ek hi taraf kyun flow karti hai.
Refrigerators and Heat Pumps — same symbols, engine ulta chala diya.
PV diagrams and Work — jahan work $W$ ek loop area ke roop mein dikhti hai.