Thermodynamic processes — isothermal (T const), isochoric (V const), isobaric (P const), adiabatic (Q = 0): Foundations

1.7.14 · D1 · Physics › Thermodynamics › Thermodynamic processes — isothermal (T const), isochoric (V

Yeh page yeh maanke chalta hai ki tumne kuch bhi nahi dekha. Har woh symbol jo parent note (parent topic) use karta hai, yahan scratch se build kiya gaya hai, uss order mein jo har ek ko pichle wale pe lean karne deta hai.

1. Gas in a box — hamara poora universe

Is chapter mein sab kuch ek ek picture ke andar hota hai: ek cylinder of gas jisme upar ek piston (ek sliding lid) hai.

Figure — Thermodynamic processes — isothermal (T const), isochoric (V const), isobaric (P const), adiabatic (Q = 0)

Yahan se kyun shuru karein? Kyunki pressure, volume, temperature aur energy sab is trapped gas ki properties hain. Figure dekho: gas shaded region hai, piston movable wall hai, aur arrows woh do cheezein dikhate hain jo boundary cross kar sakti hain — heat aur work. Woh image dimag mein rakho; neeche har symbol ussi mein rehta hai.

2. Volume $V$ — gas kitni jagah fill karta hai

Topic ko yeh kyun chahiye: chaar processes mein se do define hoti hain is baat se ki $V$ kya karta hai. "Isochoric" = $V$ frozen; expansion = $V$ increase ho raha hai. Agar tum picture mein $V$ ko point kar sako (shaded height), tum har process padh sakte ho.

$V = A \times h (face area \times column height)$

3. Pressure $P$ — gas kitna zyada dhakka deta hai

"Force over area" kyun, na ki bas "force"? Kyunki wahi dhakka dene wali gas ek wide piston pe zyada total force exert karti hai bjaaye ek narrow piston ke — lekin pressure (wall ke har patch pe push) same hota hai. Pressure ek honest, size-independent measure hai ki gas kitna zyada dhakka deta hai. Figure dekho: same particle-drumming, lekin wide piston zyada hits pakadta hai, isliye total force bada hai jabki $P$ fixed rehta hai.

$P = \frac{F}{A} (force \div jis area pe act karta hai)$

Parent note ka phrase " $P$ held fixed" (isobaric) ka matlab bas yeh hai: drumming intensity constant rakho, jaise piston pe ek fixed weight rakh ke.

4. Temperature $T$ — particles kitni tezi se hilte hain

Topic ko yeh kyun chahiye: "isothermal" = $T$ frozen. Aur $T$ woh ek number hai jo hidden internal energy control karta hai (Section 8).

5. Gas ki maatra: $n$ aur constant $R$

Kyun zaroori hai: parent ki har formula — $P V = n R T$ , $C_{P} = C_{V} + R$ , work integrals — $R$ ko is bridge ki tarah carry karta hai.

6. Ideal Gas Law — $P$ , $V$ , $T$ ko ek saath baandhna

Yeh master link hai. Yeh kehta hai ki gas ke chaar numbers independent nahi hain — koi bhi teen fix karo aur chautha forced hai. Ideal Gas Law dekho complete build ke liye.

7. Heat $Q$ — energy jo temperature gap ki wajah se wall cross karti hai

8. Internal energy $U$ aur symbol $Δ$

Topic yahan kyun lean karta hai: isliye isothermal mein $Δ U = 0$ milta hai (hence $Q = W$ ), aur isliye $Δ U = n C_{V} Δ T$ har process mein kaam karta hai, na sirf constant volume mein.

9. Work $W$ — energy jo gas piston ko push karke kharch karta hai

Figure key move dikhata hai: piston ko ek tiny slice $d x$ baahir push karo. Gas force hai $F = P A$ , aur swept volume hai $d V = A d x$ . Toh tiny work hai

$d W = F d x = P A d x = P (A d x) = P d V .$

Saare slices add karne se parent ka boxed result milta hai, $W = \int P d V$ — pressure–volume graph pe curve ke neeche area. (" $\int$ " aur " $d V$ " ka matlab agla section unpack karta hai.) Full treatment: Work done by gas — PV diagrams.

10. Calculus symbols: $d$ , $\int$ , aur $ln$

Parent teen pieces of calculus notation use karta hai. Yahan har ek ek picture ki tarah hai — pehle se koi calculus nahi chahiye.

Yeh tool kyun aur simple " $P \times Δ V$ " kyun nahi? Kyunki zyaadaatar processes ke along pressure change karta hai jaise gas expand hoti hai (curved graph dekho). Plain multiplication sirf tab kaam karta hai jab $P$ flat ho (isobaric rectangle). Integral ek changing height add karne ka honest tarika hai — yahi exactly sawaal hai "ek curve ke neeche area kya hai?" aur $\int$ uska jawab hai.

$ln$ kyun aur kuch nahi? Isothermal curve ki height $1/ V$ ke proportional hai. Ek $1/ V$ shape ke neeche area, by definition, natural log hai. Koi aur function woh area measure nahi karta — toh $ln$ humpe forced hai, style ke liye choose nahi kiya gaya.

11. Heat capacities $C_{V}$ , $C_{P}$ aur ratio $γ$

Topic ko yeh kyun chahiye: $γ$ woh single knob hai jo adiabat ki shape aur adiabatic work formula control karta hai.

12. First Law — woh balance sheet jo kabhi fail nahi hoti

Yahan har symbol ab defined hai: $Δ U$ (§8), $Q$ (§7), $W$ (§9). Yeh single line, $P V = n R T$ aur ek frozen variable ke saath combine hoke, chaar saare processes generate karta hai. First Law of Thermodynamics dekho.

13. Yeh sab topic ko kaise feed karta hai

Upar se neeche padho: chaar state numbers Ideal Gas Law build karte hain; temperature aur $C_{V}$ internal energy build karte hain; heat aur work First Law build karte hain; $γ$ aur $ln$ curves shape karte hain — aur sab kuch chaar named processes mein pour ho jaata hai.

Equipment checklist

Khud ko test karo — right side cover karo aur zyaaz se jawab do.

V

kya measure karta hai, aur kis unit mein?

Woh space jo gas fill karta hai, cubic metres

m^{3}

mein.

Pressure

P

physically kya matlab rakhta hai?

Force per unit area jo gas apni walls pe exert karta hai, pascals (

N / m^{2}

) mein.

T

kelvin mein kyun hona chahiye, Celsius mein kyun nahi?

Gas laws ko ek absolute scale chahiye jo

0 K

se shuru ho; convert karo

T_{K} = T_{° C} + 273

se.

Ek mole

n

kya hai?

Gas particles ka ek fixed count (

6.02 \times 1 0^{23}

) — gas "kitni" hai.

Ideal Gas Law batao.

P V = n R T

Heat

Q

aur internal energy

U

mein fark?

Q

energy hai jo boundary ke across flow karti hai;

U

energy hai jo gas ke andar stored hoti hai.

Δ

ka matlab kya hai?

Change = final minus initial.

Ek ideal gas ke liye,

Δ U

har process mein kya hota hai?

n C_{V} Δ T

(internal energy sirf temperature pe depend karti hai).

\int_{V_{1}}^{V_{2}} P d V

kaun si picture represent karta hai?

Pressure–volume curve ke neeche ka area = gas dwara kiya gaya work.

Isothermal work mein

ln

kyun appear karta hai?

Kyunki

P \propto 1/ V

, aur ek

1/ V

curve ke neeche area natural logarithm hai.

C_{P} > C_{V}

kyun?

Constant pressure pe heat expansion work ke liye bhi pay karta hai, toh har kelvin ke liye zyada heat chahiye.

γ

kya hai aur yeh

> 1

kyun hai?

γ = C_{P} / C_{V}

; kyunki

C_{P} > C_{V}

yeh 1 se zyada hai, jo adiabats ko isotherms se steeper banata hai.

First Law sign conventions ke saath batao.

Δ U = Q - W

: heat in positive hai, work gas dwara kiya gaya positive hai.