Heat engines — efficiency η = 1 − Q_C - Q_H

1.7.19 · Physics › Thermodynamics

Heat engine kya hota hai?

WHY the cycle matters: Ek baar ki expansion bahut saari heat ko work mein convert kar sakti hai, lekin phir gas "khatam" ho jaati hai (expand ho gayi, thandi ho gayi). Continuously chalane ke liye tumhe engine ko reset karna padta hai — aur resetting mein hamesha kuch heat dump karni padti hai.

Efficiency formula ko scratch se derive karna

Hum First Law (energy conservation) ko ek poore cycle par apply karte hain.

Step 1 — Cycle ke liye First Law likho. $\Delta U=Q_{\text{net}}-W_{\text{by gas}}$ Why this step? First Law hamesha hold karta hai; hum bas ise ek complete loop ke liye specialise kar rahe hain.

Step 2 — Yeh use karo ki internal energy ek state function hai. Ek closed cycle mein system apni starting point par wapas aa jaata hai, isliye $\Delta U_{\text{cycle}}=0$ Why this step? $U$ sirf state par depend karta hai (jaise ideal gas ke liye $T$), path par nahi. Same start = same end = zero change.

Step 3 — Net heat identify karo. Heat in hai $Q_H$, heat out hai $Q_C$ ($Q_H,Q_C>0$ magnitudes liye hue hain): $Q_{\text{net}}=Q_H-Q_C$

Step 4 — Combine karo. $\Delta U=0$ ke saath: $0=(Q_H-Q_C)-W⟹\boxed{W=Q_H-Q_C}$ Why this step? Jo bhi heat dump nahi hui woh saari work bani. Energy conserved hai.

Step 5 — Efficiency define karo "jo mila / jo diya" ke roop mein: $\eta \equiv \frac{W}{Q_H}=\frac{Q_H-Q_C}{Q_H}$

Step 6 — Simplify karo. $\boxed{\eta =1-\frac{Q_C}{Q_H}}$

Worked examples

Common mistakes (Steel-manned)

Active recall

Connections

• First Law of Thermodynamics — $W=Q_H-Q_C$ deta hai.
• Second Law of Thermodynamics — $\eta =1$ forbid karta hai (Kelvin–Planck).
• Carnot Cycle — reversible engine jo efficiency ceiling set karta hai.
• Entropy — explain karta hai kyun heat dump karni padti hai ($\Delta S_{\text{universe}}\ge 0$).
• Refrigerators and Heat Pumps — engine ulta chalaaya hua; $\eta$ ki jagah COP.
• PV diagrams and Work — cycle loop ka area = net work $W$.

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