Thermodynamics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Thermodynamics — the branch of physics dealing with heat, work, and the internal energy of systems.

First Law (Conservation of Energy): $$\Delta U = Q - W$$

Where $\Delta U$ = change in internal energy, $Q$ = heat added to system, $W$ = work done by system.

Sign convention:

Quantity	Positive	Negative
$Q$	Heat TO system	Heat FROM system
$W$	Work BY system ON surroundings	Work ON system BY surroundings
$\Delta U$	Temperature increases	Temperature decreases

Second Law: Two equivalent statements:

• Kelvin-Planck: No heat engine can be 100% efficient — some heat must be expelled to a cold reservoir
• Clausius: No refrigerator can operate without external work input

Carnot Efficiency: $$\eta = 1 - \frac{T_C}{T_H} \quad \text{(all temperatures in Kelvin)}$$

⚡ Exam tip: ALWAYS convert °C to Kelvin: $T(K) = T(°C) + 273$. A temperature of 27°C = 300 K.

⚡ Work done = area under PV curve. For a cyclic process, net work = area enclosed by the cycle.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of thermodynamic processes.

Thermodynamic Processes:

Process	Condition	ΔU	Q	W
Isothermal ($T = $ constant)	$\Delta T = 0$	$0$	$Q = W$	$W = nRT \ln(V_2/V_1)$
Adiabatic ($Q = 0$)	$\Delta Q = 0$	$\Delta U = -W$	$0$	$W = \frac{P_1V_1 - P_2V_2}{\gamma-1}$
Isochoric ($V = $ constant)	$\Delta V = 0$	$nC_V\Delta T$	$Q = \Delta U$	$0$
Isobaric ($P = $ constant)	$\Delta P = 0$	$nC_V\Delta T$	$Q = nC_P\Delta T$	$W = P\Delta V$

Adiabatic equation: $$PV^\gamma = \text{constant}, \quad \gamma = \frac{C_P}{C_V}$$

For monatomic gas: $\gamma = 5/3$. For diatomic (at room temp): $\gamma = 7/5$.

Carnot Cycle — Step by Step:

1. Isothermal expansion at $T_H$ → system absorbs heat $Q_H$, does work $W_1$
2. Adiabatic expansion → temperature drops to $T_C$, system does work $W_2$
3. Isothermal compression at $T_C$ → system expels heat $Q_C$ to cold reservoir, work $W_3$ done ON system
4. Adiabatic compression → temperature rises to $T_H$, work $W_4$ done ON system

Net work $W = W_1 + W_2 - W_3 - W_4 = Q_H - Q_C$. Net efficiency $\eta = 1 - Q_C/Q_H = 1 - T_C/T_H$.

Entropy — What It Actually Means: $$\Delta S = \int \frac{dQ_{\text{rev}}}{T}$$

Entropy measures disorder or the number of ways microscopic states can arrange. Key facts:

• For reversible process: $\Delta S_{\text{universe}} = 0$
• For irreversible (spontaneous) process: $\Delta S_{\text{universe}} > 0$
• Total entropy of universe always increases (Second Law)

Heat Engines and Refrigerators:

Heat Engine: Converts heat into work. $$\eta = \frac{W}{Q_H} = \frac{Q_H - Q_C}{Q_H} = 1 - \frac{Q_C}{Q_H}$$

Refrigerator/Heat Pump: Uses work to transfer heat from cold to hot. $$\text{COP}{\text{refrigerator}} = \frac{Q_C}{W{\text{in}}} = \frac{Q_C}{Q_H - Q_C} = \frac{T_C}{T_H - T_C}$$

Common mistakes:

• Using °C instead of Kelvin in Carnot efficiency formula
• Forgetting sign conventions: work done BY system is positive, ON system is negative
• Confusing $\Delta U$ with $Q$: only equal when $W = 0$ (isochoric)
• Forgetting that adiabatic $Q = 0$ doesn’t mean $\Delta U = 0$

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🔴 Extended — Deep Study (3mo+)

Comprehensive derivations and JEE Advanced-level problems.

Derivation: Work Done in Adiabatic Process

From first law: $\Delta U = -W$ (since $Q = 0$) For ideal gas: $\Delta U = nC_V\Delta T$ $$W = -nC_V(T_2 - T_1)$$

Using ideal gas law: $PV = nRT$ and $PV^\gamma = \text{constant}$: $$W = \frac{P_1V_1 - P_2V_2}{\gamma - 1}$$

Entropy of Mixing (Two Ideal Gases): When two different gases mix spontaneously: $$\Delta S = n_1R\ln\frac{V_2}{V_1} + n_2R\ln\frac{V_2}{V_2}$$

This is positive (entropy increases) — demonstrating the irreversibility of mixing. If gases are identical, $\Delta S = 0$ even though mixing occurred — Gibbs paradox.

Clausius Inequality: $$\oint \frac{dQ}{T} \leq 0$$

Equality holds for reversible cycles, strict inequality for irreversible cycles.

Heat Pumps: COP (heating): $\text{COP}{\text{HP}} = \frac{Q_H}{W{\text{in}}} = \frac{T_H}{T_H - T_C}$ A heat pump is just a refrigerator running in reverse. The COP is always greater than 1.

Van der Waals Equation (Real Gases): $$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$

• $a$ accounts for attractive forces between molecules (increases boiling point, critical temperature)
• $nb$ accounts for finite molecular volume (excluded volume)

Phase Change and Latent Heat: $$Q = mL$$

Latent heat of fusion (ice → water): $L_f = 334$ J/g. Latent heat of vaporisation (water → steam): $L_v = 2260$ J/g.

NEET/JEE Previous year patterns:

• First Law + sign conventions: Very frequent (1-2 questions per year)
• Carnot efficiency: Very frequent in both NEET and JEE
• PV diagram work: Very frequent (1-2 questions per year)
• Entropy: Moderate in NEET, frequent in JEE
• Adiabatic processes: Frequent in JEE Advanced
• Refrigerators/heat pumps COP: Moderate frequency in NEET
• Van der Waals equation: JEE Advanced level

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📊 NEET UG Exam Essentials

Detail	Value
Questions	200 (180 mandatory + 10 optional)
Time	3h 20min
Marks	720
Section	Physics (50), Chemistry (50), Biology (100)
Negative	−1 for wrong answer
Qualifying	50th percentile (general category)

🎯 High-Yield Topics for NEET UG

• Human Physiology — 18 marks
• Genetics & Evolution — 16 marks
• Ecology & Environment — 12 marks
• Organic Chemistry (Reactions) — 15 marks
• Electrodynamics (Physics) — 18 marks
• Chemical Equilibrium — 10 marks

📝 Previous Year Question Patterns

• Q: “A particle moves in a circle…” [2024 Physics — 2 marks]
• Q: “Identify the incorrect statement about DNA…” [2024 Biology — 4 marks]
• Q: “The major product ofFriedel-Crafts acylation is…” [2024 Chemistry — 3 marks]

💡 Pro Tips

• NCERT Biology is the single most important resource — 80%+ questions are from NCERT lines
• Focus on Human Physiology, Genetics, and Ecology — together they make ~40% of Biology
• In Physics, master Electrostatics + Current Electricity + Magnetism (combined ~20%)
• Organic Chemistry: learn named reactions with mechanisms — they repeat across years

🔗 Official Resources

• NTA Official
• NEET Syllabus PDF

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