Spontaneity — second law; entropy ΔS — Hinglish notes

2.5.12 · Chemistry › Thermodynamics (Chemical)

Entropy kaise badalti hai: thermodynamic definition

Isothermal process (constant T) ke liye ΔS derive karna: $T$ ko integral se bahar nikalo: $Δ S = \frac{1}{T} \int d q_{r e v} = \frac{q _{r e v}}{T}$

$q_{r e v}$ kyun, sirf $q$ kyun nahi? Heat ek path function hai. Ek state function paane ke liye (ΔS sirf start aur end par depend karta hai), hume reversible path pe exchange hua heat use karna padta hai — woh unique, "sabse gentle" path jo heat ko maximize karta hai. Koi bhi real (irreversible) path kam useful heat deta hai, isliye neeche inequality hai.

Thermodynamics ka Second Law

Surroundings term derive karna: surroundings constant $T$ par ek bade reservoir ki tarah kaam karte hain. System se nikli heat, $q_{sy s}$ , surroundings mein $- q_{sy s}$ ke roop mein temperature $T$ par jaati hai: $Δ S_{s u r r} = \frac{q _{s u r r}}{T} = \frac{- q _{sy s}}{T} = \frac{- Δ H _{sy s}}{T} (const P)$ Last step mein $q_{P} = Δ H$ use kiya hai.

Figure — Spontaneity — second law; entropy ΔS

Worked Examples

Forecast-then-Verify

Recall Examples padhne se pehle, forecast karo:

Gas compress hone par $Δ S$ ka sign? → negative (kam positions).
Endothermic reaction ke liye $Δ S_{s u r r}$ ka sign? → negative (surroundings heat kho dete hain).
Boiling point par, $Δ S_{u ni v} =$ ? → zero (equilibrium).

Flashcards

Thermodynamically spontaneous process kya define karta hai?

Woh jo bina continuous external intervention ke aage barhta hai; direction ke baare mein hai, speed ke nahi.

Second law ka entropy form batao.

Δ S_{u ni v} = Δ S_{sy s} + Δ S_{s u r r} \geq 0

; >0 spontaneous, =0 equilibrium, <0 impossible.

Boltzmann ka entropy equation?

S = k_{B} ln W

W

= number of microstates.

W

ki jagah

ln W

kyun?

Entropy additive honi chahiye jabki microstates multiply karte hain; log products ko sums mein badalta hai.

dS ki thermodynamic definition?

d S = \frac{d q _{r e v}}{T}

(reversible heat over temperature).

Entropy definition mein reversible heat kyun?

Heat ek path function hai; sirf reversible path ΔS ke liye ek state-function value deta hai.

Constant P par surroundings ke ΔS ka formula?

Δ S_{s u r r} = - \frac{Δ H _{sy s}}{T}

Isothermal reversible ideal-gas expansion ke liye ΔS?

Δ S = n R ln \frac{V _{2}}{V _{1}}

ΔH_fus se ΔS of fusion?

Δ S = \frac{Δ H _{f u s}}{T _{m e l t}}

Kya ek exothermic reaction non-spontaneous ho sakta hai?

Haan, agar

Δ S_{sy s}

bahut negative ho to

Δ S_{u ni v} < 0

Kya ek endothermic reaction spontaneous ho sakta hai?

Haan, agar

Δ S_{sy s}

bada positive ho (jaise NH4NO3 ka dissolving).

Reaction mein gas ke moles badhne par ΔS ka sign?

Positive.

Connections

Gibbs Free Energy ΔG — dono terms combine karta hai: $Δ G = Δ H - T Δ S$ (system-only spontaneity test).
First Law of Thermodynamics — $q_{r e v}$ aur $Δ H = q_{P}$ provide karta hai.
Enthalpy ΔH — $Δ S_{s u r r} = - Δ H / T$ ko feed karta hai.
Reversible vs Irreversible Processes — kyun $q_{r e v}$ matter karta hai.
Boltzmann distribution & microstates — $S$ ka statistical meaning.
Third Law of Thermodynamics — $0$ K par $S = 0$ set karta hai, absolute entropies deta hai.

Spontaneity — second law; entropy ΔS

Spontaneity KYA hai?

Entropy KYA hai?