1.3.10
Har real machine ek leaky bucket ki tarah hai. Aap upar se energy daalo (input), lekin kuch sides se heat, sound, friction ke roop mein leak ho jaati hai — aur sirf jo neeche ke spout se nikalta hai woh useful energy hai jo aap actually chahte the. Efficiency bas jo aapne daala uska woh fraction hai jo aapko useful form mein mila . Koi bhi machine kabhi > 100%
Energy hamesha conserved rehti hai (first law of thermodynamics) — toh phir kyu parwaah karein? Kyunki har energy utni equally useful nahi hoti. Jab 100 J bijli 90 J light aur 10 J waste heat ban jaaye, toh 100 J toh abhi bhi exist karti hai, lekin sirf 90 J ne woh kaam kiya jo aap chahte the. Efficiency woh bookkeeping tool hai jo useful output ko total input se alag karti hai, taaki hum machines compare kar sakein, energy bills kum kar sakein, aur behtar engines design kar sakein.
==Efficiency η useful energy (ya power) output aur total energy (ya power) input== ka ratio hai:
η = E total in E useful out = P total in P useful out dimensionless number hai 0 1 100
Kyunki power P = t E t η = E in / t E useful / t = P in P useful out Yeh step kyu? t
Worked example Example 1 — Electric motor ek load uthaa raha haiEk motor 500 J 5 kg 6 m η g = 10 m/s 2
Step 1 — Useful output = PE mein gain.
E useful = m g h = 5 × 10 × 6 = 300 J Yeh step kyu? Motor ne jo useful kaam kiya woh box ko upar uthana tha, isliye useful energy = gravitational PE gained.
Step 2 — Definition apply karo.
η = 500 300 = 0.6 = 60% Yeh step kyu? Input woh electrical energy hai jo supply ki gayi. Baaki 200 J
Worked example Example 2 — Power form (ek pump)Ek water pump 2 kW 1.4 kW η
Step 1 — Efficiency. η = 2.0 1.4 = 0.7 = 70% Yeh step kyu? Dono quantities same units (kW) mein powers hain, isliye seedha divide karo.
Step 2 — Wasted power. P waste = P in − P out = 2.0 − 1.4 = 0.6 kW Yeh step kyu? Conservation: input power useful + wasted mein split hoti hai.
Worked example Example 3 — Forecast-then-Verify (chained machines)Series mein do machines: machine A 80% 50% Forecast: Overall efficiency 50% (ruko aur guess karo)
Verify: Overall η = η A × η B = 0.80 × 0.50 = 0.40 = 40% Multiply kyu? B ka input hi A ka output hai. Agar 100 80 40 40/100 = 40% Lesson: Chained efficiencies multiply hote hain, aur result hamesha sabse chhote single stage se lower hota hai. Tumhara "50% se kam" wala guess sahi tha.
Common mistake "Efficiency 100% se zyada ho sakti hai agar machine bahut achhi ho."Yeh sahi kyu lagta hai: Kuch machines aise lagte hain jaise amplify karti hain — ek lever chhoti force se bada load uthane deta hai, isliye aisa lagta hai jaise "andar se zyada bahar nikal raha hai."
Fix: Lever force multiply karta hai, energy nahi. Tum zyada distance par kheencho, isliye F × d F × d η ≤ 100%
Common mistake "Wasted energy gayab ho jaati hai."Yeh sahi kyu lagta hai: Tum ise dekhte nahi, isliye lagta hai chali gayi.
Fix: Woh abhi bhi wahan hai — heat, sound, vibration ke roop mein. Energy conserved hai; "wasted" ka matlab sirf "jis form mein main chahta tha uss mein nahi" hai. E in = E useful + E wasted
Common mistake "Useful output ki jagah total output use karo."Yeh sahi kyu lagta hai: "Output toh output hi hai."
Fix: Sirf woh part count hota hai jo intended kaam kar raha ho. Ek bulb ka total output (light + heat) ≠ useful output (sirf light). Hamesha poochho: mujhe actually kya chahiye tha?
Common mistake Units convert karna bhool jaana (kJ vs J, kW vs W).Fix: Divide karne se pehle E useful E in η
What is efficiency in words? Total input energy (ya power) ka woh fraction jo useful energy (ya power) ke roop mein milta hai.
Write the efficiency formula. η = E useful out / E total in = P useful out / P in
Why can efficiency never exceed 100%? Kyunki energy conserved hai — jo daala usse zyada useful energy nahi nikal sakte.
What happens to the "wasted" energy? Woh abhi bhi conserved rehti hai, lekin unwanted forms (heat, sound, vibration) mein convert ho jaati hai, destroy nahi hoti.
For machines in series, how do efficiencies combine? Woh multiply hote hain: η total = η 1 × η 2 × …
A motor uses 500 J and gives 300 J useful. Efficiency? 300/500 = 60%
Express efficiency in terms of wasted energy. η = 1 − E wasted / E in
Is efficiency dimensioned or dimensionless? Dimensionless (ek ratio); aksar % mein dikhaya jaata hai.
Why does a lever NOT have efficiency > 100%? Woh force multiply karta hai energy nahi; tum zyada distance move karte ho, isliye energy out ≤ energy in.
Recall Feynman: 12-saal ke bachche ko samjhaoSocho tumhare paas £1 pocket money hai (woh energy jo tumne daali). Tumhe sweets chahiye, lekin dukaan ek "service fee" leta hai jo tum avoid nahi kar sakte — shayad 30p. Tumhe sirf 70p ki sweets milti hain. Efficiency hai "tumhara kitna paisa sweets mein badla" — yahan 70%. Koi bhi dukaan tumhe tumhare paise se zyada sweets nahi de sakta, isliye efficiency 100% se zyada nahi ho sakti. Woh 30p gayab nahi hua — dukandaar ke paas hai (woh machine mein heat aur noise ban gaya!).
"USE IN." Efficiency = USE ful out ÷ jo IN gaya.
Aur yaad rakho: Achhi machines cool chalti hain, buri machines hot chalti hain — heat = wasted energy.
Waste heat sound friction
Power version Puseful/Pin
