Real gas effects — dissociation, recombination: Foundations

3.3.20 · D1 · Physics › Rocket Propulsion › Real gas effects — dissociation, recombination

Ye page yeh assume karta hai ki tumhe parent topic ki notation ke baare mein kuch nahi pata. Hum har symbol ek-ek karke build karenge, aur har ek agla symbol kamayega. Akhir tak tumhe parent note bina kisi unexplained squiggle ke padhna aa jaana chahiye.

0 — Molecule kya hota hai, aur "bond" kya hota hai?

Kisi bhi symbol se pehle, picture samjho. Ek molecule atoms ka ek chhota group hota hai jo chemical bonds se juda hota hai — atoms ko balls samjho aur bond ko ek stiff spring jo do balls ko jodar hai.

Figure — Real gas effects — dissociation, recombination

Greek letter $Δ$ ("delta") ka matlab hamesha "change in" ya "amount of" hota hai. $H$ enthalpy ke liye hai — hamare liye, simply "constant pressure par heat content". Toh $Δ H_{d}$ = "bonds todne ke liye zaroori heat".

1 — Temperature $T$ aur collisions ki "wildness"

Picture: molecules uchhalti hui balls hain. Cold = halke bumps. Hot = ek doosre se takat se takrana. Jab ek takkar itni tez ho ki bond ka spring survive na kar sake, toh molecule toot jaata hai. Isliye heat dissociation karti hai.

$T_{0}$ = ek reference / starting temperature (jaise combustion se pehle).
$T_{c}$ = chamber temperature, woh temperature jo combustion chamber ke andar pahunchi jaati hai.

Chhota neeche likha letter ("subscript") sirf ek label hai. $T_{c}$ , $T$ times $c$ nahi hai — ye "woh $T$ jo chamber se belong karta hai" hai.

2 — Dissociation aur recombination ek do-taraf ke arrow ke roop mein

Ab hum do events ko naam de sakte hain.

Hum dono ko ek saath double arrow $⇌$ se likhte hain: $A_{2} ⇌ 2 A$

Seedha padho: " $A_{2}$ " ek molecule hai jo do identical atoms A se milkar bana hai jo saath jude hain. Upar ka arrow ( $\to$ ) hai do loose atoms mein tootna. Neeche ka arrow ( $\leftarrow$ ) hai unka wapas chipakna. A ke aage ka number 2 matlab "unmein se do". Kuch create ya destroy nahi hota — atoms sirf re-arrange hote hain.

3 — Degree of dissociation $α$ : ek number for "kitna toota?"

Humein 0 (kuch nahi toota) se 1 (sab kuch toota) tak ek single dial chahiye.

Picture: 100 molecules ka ek jar. Agar 10 split ho gaye hain, $α = 10/100 = 0.10$ . Saare cases cover karo:

$α = 0$ → kuch dissociated nahi (thanda gas, ya bonds zyada mazboot). Ek ordinary gas ki tarah behave karta hai.
$α = 1$ → sab kuch atoms mein toot gaya (extreme heat).
$0 < α < 1$ → asli, in-between situation rocket ke andar.

Topic ko iske zaroorat kyun hai: $α$ woh ek knob hai jo temperature, pressure aur energy ko saath jodata hai. Parent note ka har "lever" basically yehi hai ki "kuch cheez $α$ ko kaise change karti hai?"

4 — Particles ginना: moles $n$ aur molar mass $M$

Picture: $n$ ek headcount hai; $M$ per head average weight hai.

Yahan woh subtle point hai jis par poora topic tika hai. Jab ek molecule $A_{2}$ do atoms A mein split hota hai, total mass unchanged rehti hai lekin particles ki sankhya badh jaati hai (1 → 2). Toh per particle average weight — molar mass $M$ — neeche jaata hai.

Isliye baad mein exhaust actually zyada tez ho sakta hai: halka gas zyada aasani se nikalta hai.

5 — Specific heat $c_{p}$ aur enthalpy balance

$\overset{c}{ˉ}_{p}$ mein bar ka matlab sirf "averaged" hai temperature range ke upar (kyunki $c_{p}$ khud real gas mein temperature ke saath thoda badalta hai).

Ab hum parent ki core energy equation padh sakte hain. Woh kehti hai: combustion ki heat do piles mein baanti jaati hai — $Q_{co mb} = pile 1: gas ko heat karta hai n \overset{c}{ˉ}_{p} (T_{c} - T_{0}) + pile 2: bonds todhta hai α n Δ H_{d}$

Symbol by symbol:

$Q_{co mb}$ = combustion se release hone wali total heat (hamari income).
$(T_{c} - T_{0})$ = temperature rise, "hum kitna zyada garam hue."
$n \overset{c}{ˉ}_{p} (T_{c} - T_{0})$ = woh heat jo actually temperature badhane mein gayi (headcount × heat-per-degree × degrees).
$α n Δ H_{d}$ = woh heat jo bonds todne ke liye churayi gayi (fraction broken × headcount × cost per bond).

6 — Pressure $p$ aur equilibrium constant $K_{p}$

Humein ek rule chahiye jo predict kare ki kitna tootega ek given $T$ aur $p$ par. Woh rule hai equilibrium constant $K_{p}$ .

Tumhe $K_{p}$ yahan derive nahi karna — woh Chemical Equilibrium and Kp ka kaam hai. Tumhe sirf yeh padhna hai: "bada $K_{p}$ → equilibrium toote hue (right) side ko favour karta hai."

Le Chatelier's Principle se key qualitative fact:

7 — Do timescales: flow time, chemistry time, aur Damköhler number

Aakhri idea timing ke baare mein hai. Gas nozzle mein neeche bhagti hai toh thandi hoti hai; thanda hona chahta hai ki tukde wapas milen. Lekin recombination instant nahi hoti — kya tukdon ke paas time hai wapas judne ka nozzle chhorne se pehle?

Inhe ek single ratio se compare karo — Damköhler Number: $D a = \frac{τ _{f l o w}}{τ _{c h e m}}$

Dono extremes cover karo:

$D a ≫ 1$ (flow slow, chemistry fast) → kaafi time → tukde poori tarah recombine ho jaate hain → equilibrium flow, energy recover ho jaati hai.
$D a ≪ 1$ (flow fast, chemistry slow) → time nahi → tukde toote hi rehte hain → frozen flow, energy kho jaati hai.
$D a \approx 1$ → asli messy case, beech mein.

Woh single ratio decide karta hai ki stolen bond energy thrust ke roop mein wapas aayegi ya nahi.

Prerequisite map

Left side ka sab kuch right side ke ek box mein jaata hai: dissociation aur recombination rocket ki exhaust ko kaise change karte hain.

Equipment checklist

Right side dhako; jawab reveal karne se pehle zor se bol ke dekho.

Symbol

Δ H_{d}

ka kya matlab hai aur ise kis amount par measure kiya jaata hai?

Bonds todne ki energy (bond dissociation enthalpy), toode gaye molecules ke per mole measure kiya jaata hai.

T_{0}

aur

T_{c}

mein kya fark hai?

T_{0}

ek reference/starting temperature hai;

T_{c}

woh temperature hai jo combustion chamber ke andar pahunchi jaati hai.

Hum

\to

ki jagah double arrow

⇌

kyun use karte hain?

Kyunki tootna aur wapas banna ek saath hota hai — yeh ek do-taraf ka balance hai, ek-taraf ki finish nahi.

Words mein,

α

kya hai aur woh kaunsi range le sakta hai?

Degree of dissociation, woh fraction jo molecules toot gaye hain;

0 \leq α \leq 1

Jab ek molecule do atoms mein split hota hai, toh molar mass

M

upar jaata hai ya neeche, aur kyun?

Neeche — same total mass lekin zyada particles, isliye per particle average mass kam hoti hai.

Q_{co mb} = n \overset{c}{ˉ}_{p} (T_{c} - T_{0}) + α n Δ H_{d}

mein, dono piles kya represent karte hain?

Pehla pile = woh heat jo gas temperature badhane mein gayi; doosra pile = woh heat jo bonds todne ke liye churayi gayi.

\overset{c}{ˉ}_{p}

mein bar kya batata hai?

Temperature range par specific heat ki ek averaged value.

K_{p}

kya batata hai, aur woh kis par depend karta hai?

Reaction ka balance point (kitna toota vs. kitna poora); yeh sirf temperature par depend karta hai.

Pressure

p

badhane se

α

kis taraf jaata hai, aur kis principle se?

Woh

α

ghatata hai (dissociation dabata hai), Le Chatelier's principle se.

τ_{f l o w}

aur

τ_{c h e m}

kya hain?

Nozzle mein gas ka residence time, aur recombination reaction mein lagta time.

Agar

D a ≫ 1

hai, toh flow frozen hai ya equilibrium mein?

Equilibrium mein — chemistry itni fast hai ki saath reh sake, isliye bond energy recover ho jaati hai.

Agar

D a ≪ 1

hai, toh bond energy ka kya hota hai?

Woh toote bonds mein band rehti hai (frozen flow) aur thrust ke roop mein kho jaati hai.

Connections

Parent: 3.3.20 Real gas effects — dissociation, recombination (Hinglish)
Chemical Equilibrium and Kp
Le Chatelier's Principle
Adiabatic Flame Temperature
Nozzle Flow and Exhaust Velocity
Specific Impulse
Damköhler Number