First law - ΔU = q + w (chemist sign convention)

2.5.3 · Chemistry › Thermodynamics (Chemical)

Core Concept

The First Law of Thermodynamics kehta hai ki system ki change in internal energy barabar hai system ko transfer ki gayi heat aur system par kiye gaye work ke sum ke:

Yeh thermodynamic processes ke liye conservation of energy hai. Universe ki energy constant hai—agar ek system energy gain karta hai, toh surroundings use lose karte hain. System do tareekon se energy gain kar sakta hai:

Heat flow in hona (q > 0): molecules hotter surroundings se collide karte hain, speed up hote hain
Uske upar work kiya jaana (w > 0): compression molecules ko crowd aur faster move karata hai

Sign Convention: Chemist vs Physicist

CHEMIST CONVENTION (jo hum use karte hain):

q > 0: heat system DWARA absorb ki gayi (endothermic)
q < 0: heat system DWARA release ki gayi (exothermic)
w > 0: work system PAR kiya gaya (compression)
w < 0: work system DWARA kiya gaya (expansion)

Physicist convention (chemistry mein use mat karo): ΔU = q − w (system DWARA kiya gaya work positive hota hai). Hum isse isliye avoid karte hain kyunki chemists system ke perspective ki care karte hain: system ke saath kya hota hai.

Derivation from First Principles

Starting point: Ek isolated system (system + surroundings) ke liye conservation of energy.

$E_{universe} = E_{system} + E_{surroundings} = constant$

Differentials lete hain: $d E_{system} + d E_{surroundings} = 0$

Toh: $d E_{system} = - d E_{surroundings}$

System ke liye, internal energy in tareekon se change ho sakti hai:

Heat transfer ( $δ q$ ): temperature difference ki wajah se energy transfer
Work transfer ( $δ w$ ): organized force × displacement ki wajah se energy transfer

Sirf yahi do kyun? Molecular level par energy boundaries cross karne ke SIRF yahi do tareeке hain. Heat = random molecular collisions. Work = coordinated force (jaise ek piston push karna).

Ek infinitesimal process ke liye: $d U = δ q + δ w$

Ek finite process par integrate karte hain: $Δ U = \int δ q + \int δ w = q + w$

ΔU ek state function kyun hai lekin q aur w nahi?

ΔU sirf initial aur final states par depend karta hai (jaise hiking mein elevation change: sirf start/end altitude par depend karta hai, path par nahi).
q aur w liye gaye PATH par depend karte hain (jaise chali gayi distance: depend karta hai ki tum zigzag gaye ya seedha gaye).

Isliye hum $d U$ (exact differential) likhte hain lekin $δ q$ aur $δ w$ (inexact differentials).

Worked Examples

Worked example Example 2: Ideal Gas ka Isothermal Expansion

Problem: 2 mol ideal gas 300 K par isothermally expand hota hai, surroundings par 1200 J ka work karta hai. ΔU aur q find karo.

Solution:

Step 1: Ideal gas ke liye, $U = U (T)$ sirf. Isothermal → ΔT = 0 → ΔU = 0 Kyun? Ideal gas ki internal energy sirf kinetic energy hai = (3/2)nRT. T change nahi = U change nahi.
Step 2: Work system DWARA kiya gaya → w = −1200 J (chemist convention mein negative) Negative kyun? Gas ne piston ko bahar push kiya; system ne work karte hue energy lose ki.
Step 3: First law apply karo: $0 = q + (- 1200)$ $q = + 1200 J$

Physical meaning: Expand karte waqt constant temperature maintain karne ke liye (jo normally gas ko cool kar deta), heat ANDAR flow hui taaki energy lost as work ke liye exactly compensate ho sake. Energy in = energy out, toh internal energy unchanged rahi.

Common Mistakes

Deep Connection: Yeh Kyun Matter Karta Hai

First law in sab ka foundation hai:

Enthalpy definition: Constant P par, hum H = U + PV define karte hain taaki ΔH = q_p (constant pressure par heat) ho. Yeh tabhi sense banta hai KYUNKI ΔU = q + w.
Hess's Law: ΔU path-independent hai, toh hum reaction steps ko algebraically add kar sakte hain.
Calorimetry: Hum ΔU ya ΔH find karne ke liye controlled conditions (constant V ya P) mein heat (q) measure karte hain.
Carnot cycle: Efficiency limits first law se arise hoti hain jo cyclic processes par apply hoti hai (ΔU_cycle = 0).

Philosophical point: Yeh law kehta hai ki energy conserved but transferable hai. Universe ki total energy Big Bang se fix hai. Har chemical reaction, har engine, har living cell is constraint ke under operate karta hai. Hum energy create nahi kar sakte; hum sirf ise idhar-udhar move aur uska form change kar sakte hain.

Recall Ek 12-saal ke bacche ko explain karo

Socho tumhare paas ek piggy bank hai (system). Andar ka paisa "internal energy" hai. Tum do tareekon se andar ka paisa change kar sakte ho:

Koi tumhe paisa deta hai (heat q): Dadi se $5 milte hain → q = +5. Piggy bank mein ab zyada paisa hai.
Tum kaam karte ho aur paisa kamate ho (work w): Tum car dhone mein help karte ho aur $3 kamate ho → w = +3. Phir se, bank mein zyada paisa.

Ya ulta:

Tum candy kharееdte ho (heat release): Candy ke liye $2 nikalte ho → q = −2
Tum apne dost ko paisa dete ho (surroundings par work karte ho): Tum $4 loan dete ho → w = −4

First Law bas yahi kehta hai: Tumhare piggy bank mein change (ΔU) = tumhe diya gaya paisa (q) + tumne kamaya paisa (w).

Agar dadi ne tumhe $5 d i y e l e k in t u mn e$ 5 ek dost ko loan diye, toh tumhara piggy bank nahi badla (ΔU = 0), chahe paisa idhar-udhar move hua. Yeh isothermal expansion jaisa hai: heat andar aati hai, work bahar jaata hai, internal energy same rehti hai!

Connections

Internal Energy U - woh state function jo change ho rahi hai
Heat q - thermal energy transfer mechanism
Work w - mechanical energy transfer mechanism
PV work - chemistry mein main type of work: w = −Pext·ΔV
Enthalpy H - first law se define kiya gaya: H = U + PV
State functions vs path functions - kyun ΔU exact hai lekin q, w nahi
Bomb calorimetry - ΔU directly measure karta hai (constant V)
Adiabatic processes - q = 0, toh ΔU = w
Isothermal processes - ideal gas ke liye ΔU = 0
Hess's Law - ΔU ke state function hone par rely karta hai

#flashcards/chemistry

First Law of Thermodynamics chemist sign convention mein kya hai? :: ΔU = q + w, jahaan ΔU change in internal energy hai, q system dwara absorb ki gayi heat hai, w system par kiya gaya work hai.

Chemist sign convention mein, jab system heat absorb karta hai toh q ka sign kya hota hai? :: Positive (+). System mein ANDAR flow hoti heat positive hoti hai.

Chemist sign convention mein, jab system DWARA work kiya jaata hai (expansion) toh w ka sign kya hota hai?

Negative (−). System DWARA kiya gaya work matlab energy bahar jaati hai, toh w < 0.

Internal energy U ek state function kyun hai lekin heat q aur work w path functions hain?

U sirf initial aur final states par depend karta hai (jaise altitude). q aur w states ke beech liye gaye process path par depend karte hain.

Isothermal expansion undergo karne wale ideal gas ke liye ΔU kya hai aur kyun?

ΔU = 0 kyunki ideal gas ki internal energy sirf temperature par depend karti hai. Isothermal matlab ΔT = 0, toh ΔU = 0.

Ek gas 600 J heat absorb karta hai aur apne surroundings par 200 J work karta hai. ΔU kya hai?

ΔU = q + w = (+600) + (−200) = +400 J. Heat in +600 J hai, system dwara work −200 J hai.

Bomb calorimeter ΔU directly kyun measure karta hai?

Kyunki woh constant volume (rigid container) par operate karta hai, toh w = 0. Phir ΔU = q + 0 = q. Measure ki gayi heat ΔU ke barabar hoti hai.

Adiabatic compression mein, 500 J work ek gas par kiya jaata hai. q aur ΔU kya hain?

q = 0 (adiabatic matlab koi heat transfer nahi). ΔU = 0 + 500 = +500 J. Saara compression work internal energy ban jaata hai.

Ek cyclic process mein ek complete cycle ke dauran system ki energy ka kya hota hai?

ΔU = 0 ek complete cycle ke liye kyunki U ek state function hai. System initial state mein wapas aa jaata hai, toh U_final = U_initial.

Temperature change na hone ke bawajood ideal gas ke isothermal expansion mein heat input kyun zaroori hai?

Gas expansion ke dauran work karta hai (w < 0). ΔU = 0 rakhne ke liye (kyunki ΔT = 0), heat flow in honi chahiye (q > 0) balance karne ke liye: ΔU = q + w = 0.