1.7.2
Agar do bodies dono ek teesri body ke saath "kitna garam hai" par agree karti hain, toh woh ek doosre ke saath bhi agree karti hain. Temperature exactly woh property hai jo is agreement ko transitive banati hai — yeh woh "common label" hai jo equilibrium mein sabhi bodies share karti hain.
Intuition Humein ek "zeroth" law ki zaroorat kyun padiThermodynamics ke first aur second laws ka naam pehle rakha gaya tha, isse pehle ki physicists ko realize hua ki kuch aur bhi zyada basic state karna zaroori hai: woh cheez jo hume temperature define karne aur thermometer banana deti hai. Kyunki yeh logically laws 1 aur 2 se pehle aati hai, isko number zero mila (Ralph Fowler ne 1930s mein naam diya).
YEH kaunsi problem solve karta hai? Yeh guarantee karta hai ki thermometer ki reading meaningful hai: jab ek thermometer object A aur object B dono ko touch karke same value dikhata hai, toh A aur B sach mein equilibrium mein hote — bina A ko B ke directly rakhe .
Definition Thermal equilibriumDo systems thermal equilibrium mein hote hain jab, thermal contact mein rakhne ke baad (heat exchange hone deni, lekin mix nahi), unke beech koi net heat flow nahi hoti aur unki macroscopic properties (P, V) badalni band ho jaati hain.
Definition Zeroth Law of ThermodynamicsAgar system A C B usi system C A B
Symbols mein, A ∼ C A C ( A ∼ C ) and ( B ∼ C ) ⟹ ( A ∼ B )
Hum assume nahi karte ki temperature exist karti hai. Hum derive karte hain ki kuch aise cheez honi chahiye.
Intuition Step 1 — equilibrium ek equivalence relation haiRelation "∼
Reflexive: A ∼ A Symmetric: agar A ∼ B B ∼ A Transitive: A ∼ C , B ∼ C ⇒ A ∼ B yahi Zeroth Law hai.
Ek relation jo teeno properties rakhti hai woh equivalence relation kehlaati hai.
Intuition Step 2 — equivalence relation ⇒ classes ⇒ ek labelKoi bhi equivalence relation sabhi systems ko disjoint groups (equivalence classes) mein partition karti hai jahan ek class ka har member doosre har member ke saath equilibrium mein hota hai. Hum har class ko ek number attach kar sakte hain. Woh number exactly woh hai jise hum temperature T
Toh:
A ∼ B ⟺ T A = T B Transitivity ke bina, symbol T
Worked example Mercury thermometer se chai naapnaSetup: glass-mercury thermometer (C A B
C A A ∼ C T A Yeh step kyun? Motion ka rukna matlab heat flow khatam = equilibrium reach hua.Usi C B B ∼ C T B = T A Yeh step kyun? Same column height = thermometer ke T ( P , V )
Conclude karo A ∼ B koi net temperature change nahi.
Yeh step kyun? Yeh transitivity ki prediction hai: humne chai ko doodh se kabhi touch nahi karaya phir bhi hum jaante hain ki woh equilibrium mein hain.
Worked example Forecast-then-VerifyBlock A B D Forecast: A B A D D A Verify (reasoning): T A = T B = 5 ⇒ A ∼ B T D = 7 > 5 = T A
Common mistake "Zeroth law kehta hai heat hot se cold ki taraf flow karti hai."Kyun sahi lagta hai: woh sach mein ek thermodynamic fact hai aur 'basic' lagta hai. Fix: woh Second law ka consequence hai. Zeroth law kuch nahi kehta flow ki direction ke baare mein — yeh sirf equilibrium ki transitivity state karta hai (zero flow situations).
Common mistake "Agar A aur B dono C ke saath equilibrium mein NAHI hain, toh A aur B bhi ek doosre se alag hain."Kyun sahi lagta hai: transitivity "nahi" ke liye bhi symmetric lagti hai. Fix: Law sirf positive case par kaam karta hai. A ∼ C B ∼ C A B
Common mistake "Thermal equilibrium ka matlab sirf same internal energy / same heat content hai."Kyun sahi lagta hai: garam cheezein "zyada heat rakhti hain". Fix: Equilibrium ka matlab equal temperature hai, equal energy nahi. 30 °C par ek swimming pool aur 30 °C par ek cup equilibrium mein hain phir bhi vastly different amounts of internal energy rakhte hain. Temperature intensive hai; energy extensive hai.
Recall Feynman: ek 12-saal ke bachche ko explain karoTeen doston ki imagine karo. Agar Aman ki height Chetan jaisi hai, aur Bittu ki bhi height Chetan jaisi hai, toh Aman aur Bittu ki height bhi same hogi — tumhe unhe back-to-back khada bhi nahi karna. "Garm hona" bhi isi tarah kaam karta hai: ek thermometer "ruler" wala dost hai. Agar do cups thermometer mein same mark dikhayein, toh dono cups equally garam hain, chahe tumne unhe kabhi ek saath touch na kiya ho. Woh shared mark hi temperature hai.
"Same friend ⇒ same temp."
Teen bodies, ek matchmaker hai (C A B C R eflexive, S ymmetric, T ransitive → "RST = Really Sets Temperature ".)
Zeroth law of thermodynamics state karo. Agar A thermal equilibrium mein hai C ke saath, aur B thermal equilibrium mein hai C ke saath, toh A thermal equilibrium mein hai B ke saath.
Ise "zeroth" law kyun kehte hain? Yeh logically 1st aur 2nd laws se zyada fundamental hai (yeh temperature define karta hai), lekin unke baad formalize hua, isliye ise number 0 mila.
Zeroth law humein kaun si quantity define karne deta hai? Temperature — woh common label jo sabhi systems share karte hain mutual thermal equilibrium mein.
Thermal equilibrium ko equivalence relation banane wali teen properties kaunsi hain? Reflexive, symmetric, aur transitive (transitivity = Zeroth law).
Thermometer example mein C ka role kaun play karta hai? Thermometer khud — common reference system.
True/False: Zeroth law heat flow ki direction batata hai. False — direction (hot→cold) Second law se aati hai; Zeroth law sirf equilibrium (zero flow) se concerned hai.
Kya equal temperature ka matlab equal internal energy hai? Nahi. Temperature intensive hai; internal energy extensive hai (substance ki amount par depend karti hai).
Mathematically, A∼B ⟺ ? T A = T B
Transitivity of equilibrium
Thermal equilibrium: no net heat flow
