1.7.18 · D1Second law — Kelvin-Planck statement, Clausius statement
Energy kabhi lost nahi hoti (yahi First Law hai), lekin energy ka ek preferred direction hota hai flow karne ka: heat apne aap hot se cold ki taraf jaati hai, aur koi bhi machine ise perfectly free mein undo nahi kar sakti. Second Law bas usi one-way street ki bookkeeping hai — aur neeche jo kuch bhi hai, woh wahi vocabulary hai jo ise precisely state karne ke liye chahiye.
Kelvin–Planck aur Clausius statements ko padhne se pehle, words aur symbols ka ek poora toolbox tumhare liye already kuch matlab rakhna chahiye. Yeh page har ek ko kuch nahi se build karta hai, us order mein jisme woh ek doosre par depend karte hain. Yahan kuch bhi assume nahi kiya gaya hai — agar parent note ne ise use kiya, toh hum ise define karte hain.
Yeh Second Law topic ka foundations note hai.
U Plain words: kisi cheez ke andar stored total hidden jiggling energy — uske wildly moving molecules ki kinetic energy, plus unke beech ke springs mein locked energy.
The picture: ek box full of tiny balls bouncing around. Fast balls = hot = bada U U Topic ko kyun chahiye: Second Law is about what happens to energy as it moves. U andar baitha rehta hai.
Q Plain words: energy jo temperature difference ki wajah se flow karti hai. Yeh energy in transit hai, koi aisi energy nahi jo ek body "rakhti" hai.
The picture: do boxes touch kar rahe hain — ek mein fast balls, ek mein slow. Fast box slow box ke saath wall ke paar jiggle share karta hai. Woh flowing jiggle hi Q Kyun: dono Second-Law statements literally rules hain ki Q
W Plain words: energy jo ek push se distance par transfer hoti hai — ek ordered, useful, mechanical form. Wheel ghoomana, weight uthana, piston chalana.
The picture: ek gas piston ko baahir ki taraf push kar rahi hai. Piston move karta hai; baahir kuch lift hota hai. Woh organised energy hi W Sign convention (ise abhi fix karo, hamesha ke liye raho): is page mein W system dwara uske surroundings par kiya gaya work . Toh W > 0 W < 0 andar push karte hain (use mein work supply ki ja rahi hai, jaise ek fridge mein).
Kyun: engine ka poora kaam messy heat Q W
Figure s01 — Heat vs Work across a boundary. Left side par teal arrow heat Q W
Intuition Heat vs work — key contrastQ W ek boundary cross karti hai. Fark hai order : work coordinated hai (saari pushing ek taraf point karti hai), heat disordered hai (har direction mein jiggle). The Second Law is really about the price of turning disorder into order.
Definition Thermal reservoirPlain words: ek object itna enormous ki tum usme heat daal sako ya nikal sako bina uske temperature ko bilkul bhi change kiye.
The picture: samundar. Ek garam chamach daalo — samundar measurably garm nahi hota.
Kyun: statements kehti hain "a single reservoir," "hot reservoir," "cold reservoir." Hume aisi bodies chahiye jinका temperature fixed rahe taaki hum cleanly do steady temperatures ke beech heat flow ke baare mein baat kar sakein.
Hum hot reservoir temperature aur heat ke liye subscript H cold ke liye subscript C
Q H hot reservoir ke saath exchanged heat.Q C cold reservoir ke saath exchanged heat.
Common mistake "Subscript mujhe sign batata hai."Nahi — H C kaunsa reservoir . Woh heat andar jaati hai ya baahir, yeh machine par depend karta hai. Is topic mein hum yeh convention adopt karte hain ki Q H , Q C W magnitudes ke roop mein likhe jaate hain — positive numbers — aur har flow ki direction words mein boli jaati hai ya diagram ke arrows se dikhaayi jaati hai.
Definition Cyclic process (a cycle)Plain words: ek process jo bilkul usi state mein khatam hoti hai jahan se shuru hui thi — same pressure, same volume, same internal energy U The picture: ek pressure–volume graph par ek closed loop. Ek point se start karo, idhar-udhar ghoom, usi point par wapas aao.
Topic ko kyun chahiye: har forbidden machine ek cyclic device hai. Ek one-shot trick jo alag state mein khatam hoti hai count nahi karti. Yahi ek word "isothermal expansion converts all heat to work" objection ko defuse karta hai.
Figure s02 — A cycle as a closed loop. Orange curve machine ka pressure–volume graph par path hai; teal arrows travel ki direction dikhate hain; plum dot woh single point hai jahan path start aur khatam hota hai, toh ek loop mein Δ U = 0
Intuition "Cycle" secret hero kyun haiEk straight-line expansion mein gas apni saari absorbed heat ko work mein convert kar sakti hai — lekin woh badi ho jaati hai, aur tum ise bina reset kiye dobara nahi chala sakte. Reset karne mein work lagti hai aur heat dump hoti hai. Only over a closed loop is the accounting honest, aur sirf tabhi full heat-to-work conversion impossible ho jaata hai.
Δ Plain words: Δ X X The picture: kisi quantity ki start-height se end-height tak ek arrow.
Q net Plain words: poore cycle mein system mein add hone wali total heat — jitna usne absorb kiya minus jitna usne reject kiya.
In symbols (magnitudes use karte hue): Q net = Q H − Q C Iske liye naam kyun chahiye: neeche ki cycle derivation saari heat crossings ko is ek bookkeeping number mein add karti hai.
Intuition Cycle ke liye magic simplificationEk cycle mein system apne start par wapas aata hai, toh uski internal energy bhi wapas aati hai: Δ U = 0 0 = Q net − W ⟹ W = Q net = Q H − Q C . work equals heat-in minus heat-out — parent note mein har engine calculation mein use hoti hai.
Δ U = Q − W First law of thermodynamics dekho.
η Plain words: tumne jo heat pay ki (Q H W positive magnitudes hain.
The picture: Q H W Q C Kyun: Kelvin–Planck statement exactly yahi claim hai ki "η 1
Figure s03 — The efficiency pie. Teal bar paid heat Q H = 800 W = 500 Q C = 300 η = 0.625
Worked example Pie padhnaAgar Q H = 800 Q C = 300 W = 500 η = 500/800 = 0.625 62.5%
Definition Coefficient of performance (COP)Plain words: refrigerator ke liye, woh heat ka ratio jo tumne cold room se nikali (Q C work jo tumne pay ki (W Q C W positive magnitudes hain.
The picture: tum ek chota W Q C Kyun: Clausius statement yahi claim hai ki "tum kabhi W = 0 Q C infinite COP wali fridge forbidden hai.
Common mistake "Fridge ke liye First Law meinW Signed First Law Δ U = Q − W supply ki jaati hai iske liye, toh wahan W negative hai. Lekin magnitude COP formula COP = Q C / W positive number hai. Same physical work, do bookkeeping styles: signed First Law ke liye, magnitudes engine/fridge scorecards ke liye. Hamesha poochho: kya main signed mode mein hoon ya magnitude mode mein?
Q H W W > 0 Q C
Definition Refrigerator / heat pumpWork W W < 0 Q C Q H = Q C + W
Mnemonic Engine vs fridge arrowsEngine: heat girta hai hot→cold, work tapakta hai baahir.
Fridge: work heat ko drive karta hai cold→hot, uphill.
Related machines aur unki limits Carnot engine and Carnot theorem mein study ki jaati hain.
Definition Spontaneous processPlain words: kuch aisa jo apne aap hota hai , bina baahri push ke. Heat ka hot→cold flow karna spontaneous hai; cold→hot nahi.
Kyun: Clausius cold→hot transfer ko sole effect ke roop mein forbid karta hai — yaani spontaneously.
Definition Reversible vs irreversibleReversible: ek process jo tum backward chala sako aur koi nishaan na chhodo — film reverse mein chalao toh theek lagti hai. Irreversible: ise backward chalane ke liye Second-Law-violating miracle chahiye.
Kyun: poora Second Law yahi statement hai ki real world irreversible hai; time ka ek direction hai. Reversible and irreversible processes aur Arrow of time dekho.
Is one-way-ness ka deeper measure — entropy — Entropy and the Clausius inequality mein build hota hai.
Neeche ka map bottom-up as a dependency chain padho: teen raw quantities (U Q W cycle ka idea, First Law mein combine hote hain; First Law plus reservoir–engine picture efficiency η reservoir–fridge picture COP deta hai; η spontaneous flow ke saath) dono single Second Law ko feed karte hain. Har arrow ka matlab hai "tumhe tail box chahiye pehle head box sense karne ke liye."
Clausius no free cold to hot
Apne aap ko test karo — right side cover karo aur reveal karne se pehle jawab do.
Internal energy U System ke jiggling molecules ki total hidden kinetic-plus-potential energy.
Heat Q W Q W
Is page par W W system karta hai; W > 0 W < 0
Thermal reservoir kya hota hai? Ek body itni badi ki uska temperature fixed rehta hai chahe heat add ya remove ki jaaye.
Subscripts H C Yeh hot aur cold reservoirs ko label karte hain; Q H , Q C W
Ek cycle mein Q net Loop mein add ki gayi total heat, Q net = Q H − Q C
Cyclic process ko kya define karta hai, aur yahan yeh kyun matter karta hai? System exactly apni starting state par wapas aata hai (Δ U = 0 η = 1
First Law aur uska cycle form state karo. Δ U = Q − W Δ U = 0 W = Q net = Q H − Q C
Efficiency η η = W / Q H = ( Q H − Q C ) / Q H = 1 − Q C / Q H
COP kya hai aur kaunsi machine ise use karti hai? COP = Q C / W
Fridge ke liye First Law aur COP formula mein W Signed First Law mein W < 0 W
Spontaneous cold→hot transfer kyun forbidden hai? Kyunki yeh bina kisi aur effect ke heat ko uphill move karega — ek Clausius violation; sirf work-driven uphill flow allowed hai.
