1.7.13
First Law bas conservation of energy kahin na kahin jaayegi . Ya to (1) gas ki internal energy badhegi
(molecules tezi se hilenge → zyada hot), ya (2) gas ek piston ko bahar push karke kaam karegi.
Aur kuch nahi. Yahi poora law hai.
Definition Teeno quantities
U internal energy : total microscopic energy (kinetic + potential of saare molecules). Ek state function — sirf current state ( P , V , T ) Q heat : energy jo temperature difference ki wajah se transfer hoti hai. Ek path function hai (depend karta hai ki tum wahaan kaise pahunche).W work : energy jo gas dwara surroundings ko push karne se transfer hoti hai (volume change). Ye bhi ek path function hai.
U Q W Paani ka level (U abhi ki property hai.
Lekin "baarish mein aana" (Q W processes hain — tum
same level tak bahut saari baarish & bahut saare outflow se, ya thode-thode se pahunch sakte ho.
d U exact differential hai; d Q d W inexact hain (isliye aksar
δ Q δ W
Definition Physics (IUPAC-vs-Clausius) convention — JEE/NEET & zyaadatar physics books mein use hoti haid U = d Q − d W
Symbol
Positive jab…
Matlab
Q > 0 heat gas MEIN add ho
gas heat absorb karta hai
Q < 0 heat gas SE remove ho
gas heat release karta hai
W > 0 gas surroundings par kaam kare (expand ho, d V > 0
energy gas se bahar jaati hai
W < 0 surroundings gas par kaam karein (compress ho, d V < 0
energy gas mein aati hai
Common mistake Steel-man: "Chemistry meind U = d Q + d W Kyun sahi lagta hai: Chemists Δ U = Q + W Sachai: Ye same physics hai, bas W
Physics: W gas dwara → d U = d Q − d W
Chemistry: W gas par → d U = d Q + W on W by = − W on Δ U Fix: Sign plug karne se pehle hamesha pucho "Kiska kaam — gas dwara ya gas par?"
Common mistake Steel-man: "Compression matlab mein energy add kar raha hoon, toW Kyun sahi lagta hai: Compress karna does gas mein energy pump karta hai — positive lagta hai.
Sachai: Physics convention mein W gas dwara . Compression ke dauran
d V < 0 W = ∫ P d V < 0 Energy in dikhti hai − W > 0 d U = d Q − d W Fix: d V
Worked example Example 2 — Compression ke saath heat releaseEk gas compress hoti hai, surroundings us par 150 90 Δ U
Signs: Gas par kaam = 150 W by = − 150 Q = − 90 Kyun? Hamare formula mein W Apply karo: Δ U = Q − W = ( − 90 ) − ( − 150 ) = + 60 Kyun? 150 J pump in, 90 J heat ke roop mein bahar → net +60 J store hua.
Worked example Example 4 — Adiabatic processEk gas adiabatically compress hoti hai; us par 200 Δ U
Key fact: Adiabatic ⇒ Q = 0 W by = − 200 Kyun? Adiabatic mein koi heat exchange nahi; compression kaam hai gas par .Apply karo: Δ U = 0 − ( − 200 ) = + 200 heat up hoti hai .
Kyun? Energy sirf kaam se aa sakti hai; sab internal energy mein store ho jaati hai.
Intuition Agar sirf ye yaad rakho
d U = d Q − d W W gas dwara = ∫ P d V U T Q , W Special cases: isothermal → Δ U = 0 Q = 0 W = 0 W = P Δ V
"QUWe by" → Δ U = Q − W W gas dwara .
Socho: Q ueue (heat line lagaake andar aane ke liye) minus gas ka W alking out
(piston bahar push karna = bahar jaana). Jo andar rehta hai = Δ U
Recall Feynman: ek 12-saal ke bachche ko samjhaoSocho tumhara pet gas ka ek balloon hai. Khana khaana = heat Q andar jaana.
Wo energy ya to tumhe andar se garam karti hai (Δ U ya tumhe
push karne aur cheezein uthane detaa hai (W . Agar tum 500 calories khao aur push-ups
karte hue 200 burn karo, 300 stored rehti hain. Yahi First Law hai: *jo tum khaate ho = jo tum store karte ho
jo tum spend karte ho.* Aur "andar ki garmahat" sirf is par depend karti hai ki tum abhi kitne hot ho,
is par nahi ki kaise hot hue — lekin "khaana khaya" aur "kaam kiya" journey par depend karte hain.
Physics convention mein First Law batao Δ U = Q − W W
U Ye sirf current state ( P , V , T )
Q W Ye processes describe karte hain; inki values is par depend karti hain ki system kaise change hua, sirf endpoints par nahi.
d W = P d V Piston par gas ki force = P A = P A d x = P d V A d x = d V
Gas expand hone par W Positive (d V > 0
Gas compress hone par W Negative (d V < 0
Isothermal ideal-gas process ke liye, Δ U = ? Zero, kyunki U T T
Adiabatic process mein kaun sa term zero hota hai Q = 0 Δ U = − W
Chemistry Δ U = Q + W Nahi; wahaan W = − W by
500 200 Δ U 500 − 200 = + 300
