Phase rule — Gibbs phase rule: Question bank — Hinglish deep dive

2.4.7 · D5 · Physics › Thermodynamics & Statistical Mechanics (Advanced) › Phase rule — Gibbs phase rule

True or false — justify

Do immiscible liquids ek beaker mein ek liquid phase count hoti hain.

False — wo do phases hain; ek phase ek distinct homogeneous region hoti hai jise tum mechanically alag scoop kar sako, aur oil aur water mix nahi karte, isliye

P

ko unse

+ 2

milta hai,

+ 1

nahi.

Ek supersaturated solution jismein koi solid present nahi hai, ek single phase hai.

True — jab tak koi doosra homogeneous region actually form nahi hua, ek uniform liquid region hai, isliye

P = 1

; metastability koi phase create nahi karti.

F = C - P + 2

mein "

2

" ko "

3

" se replace kiya ja sakta hai agar hum electric field ko bhi vary hone dein.

True in principle — constant sirf freely variable global intensive fields count karta hai; ek magnetic ya electric field add karna jo sab phases par act kare ise raise kar deta hai, deta hai

F = C - P + 3

Pressure ko 1 atm par fix karna rule ko

F = C - P + 1

bana deta hai.

True — tumne do global knobs mein se ek hata diya, isliye condensed phase rule Condensed phase rule apply hoti hai; sirf

T

aur compositions free rehte hain.

Ek chemical species add karna hamesha components ki sankhya

C

badhata hai.

False — agar nayi species dooson se ek equilibrium reaction ya stoichiometric constraint se bandi hui hai, toh

C

wahi rehta hai ya count unaffected hoti hai, kyunki

C = species - reactions - constraints

Ek pure substance ke triple point par tum temperature thodi si nudge kar sakte ho.

False —

F = 1 - 3 + 2 = 0

matlab har knob locked hai; triple point

P

–

T

plane mein ek single fixed dot hai, isliye koi bhi change teen phases mein se ek ko destroy kar deta hai.

F

kabhi negative nahi ho sakta.

True — negative

F

ka matlab hoga variables se zyada constraints, yaani ek over-determined system, isliye

C

aur

P

ka woh combination simply equilibrium mein exist nahi kar sakta.

Do solid polymorphs (graphite aur diamond) coexist kar rahein hain toh ek solid phase count hote hain.

False — alag crystal structures alag phases hain; graphite + diamond

P = 2

hai chahe dono "solid carbon" hain.

Water ki boiling line ke saath,

T

choose karne ke baad bhi tum

P

choose karne ke liye free ho.

False —

C = 1

P = 2

ke saath

F = 1

milta hai; tum ek choose karte ho aur doosra (vapour pressure) Clausius–Clapeyron equation se force ho jaata hai.

Spot the error

CaC O_{3} ⇌ CaO + C O_{2}

mein 3 species hain, isliye

C = 3

Reaction ka equilibrium constant teeno amounts ko link karta hai, ek independence hata deta hai, isliye

C = 3 - 1 = 2

; species count component count nahi hoti.

"Pure water high enough pressure par chaar coexisting phases dikhaa sakta hai."

Ek one-component system ke liye

F = 0

pehle hi

P

3

par cap kar deta hai (

0 = 1 - P + 2

); tum sirf swap kar sakte ho kaun se phases hain (jaise ek high-pressure ice polymorph ordinary ice ki jagah le le), chaar ek saath kabhi nahi.

"Phase diagram ka ek area

F = 1

hai kyunki tum ek surface ke saath move karte ho."

Ek area two-dimensional hota hai, isliye

F = 2

correspond karta hai (dono

T

aur

P

free); ek line

F = 1

hai aur ek point

F = 0

hai.

"Paani mein namak daalna

C = 1

deta hai kyunki woh still 'water with stuff in it' hai."

NaCl aur

H_{2} O

chemically independent hain bina kisi linking reaction ke, isliye

C = 2

; liquid ki composition specify karne ke liye dono chahiye.

"Equilibrium constraint yeh hai ki

μ_{i}

har phase mein equal ho, isliye yeh ek equation per component hai."

P

phases ke liye yeh chain of

P - 1

independent equalities per component hai, total

C (P - 1)

constraints deta hai — per component ek nahi.

"Mechanical aur thermal equilibrium extra constraints dete hain jo humein subtract karne chahiye."

Wo already built in hain — equal

P

aur equal

T

hi wajah hai ki hum sirf ek shared

P

aur ek shared

T

count karte hain; sirf chemical potential equalities ko naye constraints ke roop mein subtract kiya jaata hai.

"Kyunki ek phase mein mole fractions

C

numbers hain, isliye har phase

C

composition variables add karta hai."

Fractions ka sum 1 hona chahiye, isliye ek dependent hota hai; har phase sirf

C - 1

independent composition variables contribute karta hai.

Ek phase ka har composition variable ek chemical-potential equality se match hota hai jo use remove karta hai, isliye phase–component product variables aur constraints mein identically enter hota hai aur subtract ho jaata hai, clean

C - P + 2

chhod ke.

Equilibrium par phases mein chemical potentials equal kyun hone chahiye?

Chemical potential mein inequality matter ko high

μ

se low

μ

ki taraf flow karne par majboor karti jab tak equalize na ho jaaye; stationary equilibrium isliye require karta hai har component ke liye equality. Dekho Gibbs free energy and equilibrium.

Har additional coexisting phase

F

ko ek se kyun reduce karta hai?

Har nayi phase

C - 1

composition variables add karti hai lekin

C

naye equilibrium equations (per component ek), net loss ek degree — formula mein

- P

Ek reaction component count ko badhane ki bajaye kyun reduce karta hai?

Reaction ki equilibrium condition species ke chemical potentials ke beech ek equation hai, unke amounts ko together tie karta hai, isliye ek species ab independent nahi rehti — dekho Components and independent reactions.

Triple point ek temperature standard ke roop mein kyun useful hai?

F = 0

ke saath yeh fully self-fixing hai — nature exactly ek

T

aur ek

P

reproduce karta hai three-phase coexistence ke liye, isliye koi external calibration knob use drift nahi kar sakta.

Har phase ki amount phase rule mein kyun appear nahi hoti?

F

sirf intensive variables count karta hai; kitne grams ice versus water hai yeh

T

P

, ya koi composition ratio change nahi karta, isliye phase ka extent variance ke liye irrelevant hai.

Edge cases

Ek pure component ke single gas phase ke liye

F

kya hai?

F = 1 - 1 + 2 = 2

— dono

T

aur

P

freely adjustable hain, jo pure-substance phase diagram par two-dimensional gas region se match karta hai.

Agar ek two-component system constant pressure par held hai aur teen phases dikhata hai, toh

F

kya hai?

Condensed rule use karke

F = C - P + 1 = 2 - 3 + 1 = 0

— coexistence invariant hai, jaise fixed-pressure alloy diagram par ek eutectic point.

Kya

F

components ki sankhya se zyada ho sakta hai?

Haan single phase ke liye:

F = C - 1 + 2 = C + 1

, isliye ek phase ke saath tumhare paas components se ek zyada degree of freedom hai (extra ek yeh hai ki dono

T

aur

P

free rehte hain).

Azeotrope ya congruently melting compound ke liye rule ka kya hota hai?

Ek extra composition constraint (do phases same composition share karte hain) ek degree remove karta hai, isliye aise special points reduced-variance features ki tarah behave karte hain chahe raw

C

aur

P

counts ordinary lagte hon.

Ek inert gas jo kisi phase mein dissolve nahi hoti,

F

badhalti hai kya?

Agar wo apna gas phase banati hai aur ek genuine independent species hai toh yeh dono

C

aur

P

mein add hoti hai; agar wo truly inert hai aur har jagah absent hai toh yeh simply system ka part nahi aur count nahi hoti.

Ek one-component system ke liye zero phases ke saath variance kya hai?

Question degenerate hai — at least ek phase exist karna chahiye physical state ke liye, isliye

P \geq 1

hamesha;

P = 0

koi matter describe nahi karta aur rule apply nahi hota.

C = 1

ke liye,

(P, F)

pairs aur unka geometric meaning list karo.

(1, 2)

= area,

(2, 1)

= line,

(3, 0)

= point;

P

badhana dimension mein neeche walk karta hai jab tak sab knobs triple point par lock na ho jaayein.

Connections

Chemical potential — $μ_{i}^{(α)} = μ_{i}^{(β)}$ ke through har equilibrium constraint supply karta hai.
Components and independent reactions — reactions $C$ ko kaise shrink karte hain.
Condensed phase rule — constant-pressure variant $F = C - P + 1$ .
Phase diagrams of pure substances — jahan areas, lines aur points rehte hain.
Clausius–Clapeyron equation — two-phase line ke saath forced $P (T)$ .
Gibbs free energy and equilibrium — equal chemical potentials equilibrium kyun mean karte hain.

Question bank — Phase rule — Gibbs phase rule