Refrigerators and heat pumps — COP — Hinglish notes

1.7.20 · Physics › Thermodynamics

Physically kya ho raha hai

Figure — Refrigerators and heat pumps — COP

Energy balance derive karna (KAISE)

COP ko first principles se define karna

Best possible: Carnot (reversible) COP

Common mistake Common errors ko steel-man karna

1. "Carnot formula mein Celsius use karna." Lagta sahi hai kyunki room temp hum °C mein measure karte hain. Lekin $Q \propto T$ entropy $Q / T$ se aata hai, jo sirf absolute scale par valid hai. Fix: hamesha kelvin mein convert karo: $T (K) = T (° C) + 273$ .

2. "COP 1 se kam hona chahiye, jaise efficiency." Lagta sahi hai kyunki engine efficiency $η < 1$ hoti hai. Lekin COP moved heat ÷ paid work hai, aur tum kaam se bahut zyada heat move kar sakte ho — isliye COP usually > 1 hota hai. Fix: COP efficiency nahi hai; ye ek leverage ratio hai.

3. "Refrigerator aur heat pump ka COP same hota hai." Same machine use hoti hai, isliye same lagta hai. Lekin numerator alag hota hai ( $Q_{C}$ vs $Q_{H}$ ). Fix: yaad rakho $COP_{h p} = COP_{r e f} + 1$ .

4. "Sign confusion: $W = Q_{C} - Q_{H}$ ." Fix: device hot mein cold se zyada heat dump karta hai; surplus paid kaam hai, isliye $W = Q_{H} - Q_{C} > 0$ .

Recall Feynman: 12 saal ke bacche ko samjhao

Heat naturally hot se cold ki taraf jaati hai, jaise ball neeche dhalaaan par girti hai. Ek fridge ek choti pump hai jo "heat-ball" ko wapas upar dhakelti hai — andar ke thande se baahri garam room mein. Upar dhakelne mein mehnat lagti hai, isliye tum plug in karte ho aur bijli se pay karte ho. COP bas ye kehta hai: "har mehnat ke liye maine kitni heat-balls upar pahunchaayi?" Ek accha fridge har push mein bahut saari balls le jaata hai, isliye uska COP bada number hota hai. Aur heat pump wohi machine hai, bas ab tum room mein khade ho aur saari heat enjoy karte ho jo wo dump karta hai — tumhari mehnat bhi warmth mein badal jaati hai!

Refrigerator cycle ke liye first law (positive magnitudes)

Q_{H} = Q_{C} + W

, kyunki

Δ U_{cy c l e} = 0

Refrigerator ka COP

COP_{r e f} = \frac{Q _{C}}{W} = \frac{Q _{C}}{Q _{H} - Q _{C}}

(fayda = cooling).

Heat pump ka COP

COP_{h p} = \frac{Q _{H}}{W} = \frac{Q _{H}}{Q _{H} - Q _{C}}

(fayda = heating).

Dono COPs ke beech relation

COP_{h p} = COP_{r e f} + 1

Refrigerator ka Carnot COP

\frac{T _{C}}{T _{H} - T _{C}}

T

kelvin mein.

Heat pump ka Carnot COP

\frac{T _{H}}{T _{H} - T _{C}}

T

kelvin mein.

COP aksar 1 se zyada kyun hota hai?

Ye moved heat per paid work hai, converted energy ka fraction nahi; tum kaam se zyada heat move kar sakte ho.

Heat ratio dene wali reversible condition

Δ S_{u ni v er se} = 0 \Rightarrow Q_{C} / T_{C} = Q_{H} / T_{H} \Rightarrow Q_{H} / Q_{C} = T_{H} / T_{C}

Bade temperature gap ka COP par asar

COP ghatta hai (denominator

T_{H} - T_{C}

barta hai).

Heat pump 1:1 electric heater se behtar kyun hai

W

ko heat ke roop mein deliver karta hai AUR bahar se extra heat

Q_{C}

kheenchta hai, isliye

COP_{h p} > 1

Connections

Heat Engines and Efficiency — refrigerator ek heat engine hai ulta chala hua; $η$ aur COP same $Q_{H}, Q_{C}, W$ share karte hain.
Carnot Cycle — maximum COP aur entropy condition deta hai.
Second Law of Thermodynamics — COP = ∞ aur bina kaam ke cold→hot heat flow ko forbid karta hai.
Entropy — $Q / T$ bookkeeping reversible heat ratio ko underlie karti hai.
First Law of Thermodynamics — $Q_{H} = Q_{C} + W$ ka source.