PhysicsPHY 05
Thermodynamics & Kinetic Theory
First/second law of thermodynamics, Carnot engine, KMT, mean free path, specific heats
NCERT XI Ch.12–13
NCERT Ref
Concept Core
Essential theory — everything NCERT tests on Thermodynamics & Kinetic Theory
ZEROTH & FIRST LAW
Zeroth law: Thermal equilibrium and temperature definition (basis of thermometers).
First law: ΔU = Q − W. Q = heat added, W = work done by system. For cyclic process: ΔU = 0 → Q = W.
Processes: Isothermal (ΔT=0, ΔU=0), Adiabatic (Q=0), Isobaric (ΔP=0), Isochoric (ΔV=0, W=0).
SECOND LAW & CARNOT ENGINE
Second law: Heat cannot spontaneously flow cold→hot. Entropy of universe always increases.
Carnot efficiency: η = 1 − TC/TH (in Kelvin). Maximum possible efficiency. Real engines always less efficient. Carnot cycle: 2 isothermal + 2 adiabatic processes.
KINETIC MOLECULAR THEORY
Assumptions: Point masses, elastic collisions, random motion, no intermolecular forces.
PV = nRT. KE per molecule = (3/2)kT. RMS speed: vrms = √(3RT/M). Mean speed: vavg = √(8RT/πM). Most probable: vmp = √(2RT/M). Order: vmp < vavg < vrms.
SPECIFIC HEATS OF GASES
Cv = (f/2)R, Cp = Cv + R, γ = Cp/Cv.
Monatomic (f=3): Cv=3R/2, Cp=5R/2, γ=5/3. Diatomic (f=5): Cv=5R/2, Cp=7R/2, γ=7/5. Polyatomic (f=6): γ→1.
MEAN FREE PATH & REAL GASES
Mean free path λ = 1/(√2 πnd²). Decreases with pressure, increases with temperature.
Van der Waals equation: (P + a/V²)(V − b) = RT. a = intermolecular attraction. b = excluded volume. Real gas → ideal at high T, low P.
Fact & Formula Vault
High-yield facts, numbers, and formulas
Key Formulae
ΔU = Q − W (First Law)
η = 1 − Tc/Th (Carnot)
PV = nRT (ideal gas)
KE per molecule = 3/2 kT
Speed Relations
v_rms = √(3RT/M)
v_avg = √(8RT/πM)
v_mp = √(2RT/M)
Order: v_mp < v_avg < v_rms
Specific Heats
Monatomic: γ = 5/3
Diatomic: γ = 7/5
Cp − Cv = R (always)
f = degrees of freedom
Worked Examples
NEET-style questions solved step-by-step
EASYFor an isothermal process, which of the following is true?▾
For an isothermal process, which of the following is true?
Temperature constant → ΔU = 0 (for ideal gas, U depends only on T). By first law: Q = W. All heat added = work done by gas.
MEDIUMA Carnot engine operates between 600K and 300K. Efficiency?▾
A Carnot engine operates between 600K and 300K. Efficiency?
η = 1 − Tc/Th = 1 − 300/600 = 1 − 0.5 = 50%. Always use Kelvin (K), not Celsius.
HARDRatio of rms speeds of O₂ (32 g/mol) and H₂ (2 g/mol) at same T?▾
Ratio of rms speeds of O₂ (32 g/mol) and H₂ (2 g/mol) at same T?
v_rms ∝ 1/√M. v_O₂/v_H₂ = √(M_H₂/M_O₂) = √(2/32) = √(1/16) = 1:4. H₂ moves 4x faster.
Mistake DNA
Common NEET traps for this chapter
⚠ Carnot temp in Celsius
Carnot efficiency formula requires ABSOLUTE temperature (Kelvin), not Celsius.
✓ Fix: Always convert to K: K = °C + 273
⚠ v_rms vs v_avg order
v_mp < v_avg < v_rms. Most probable < Average < RMS. Ratio ≈ 1 : 1.13 : 1.22.
✓ Fix: Mnemonic: PAR (Probable→Average→RMS, increasing)
⚠ Isothermal vs adiabatic ΔU
Isothermal: ΔT=0 → ΔU=0. Adiabatic: Q=0 → ΔU = −W.
✓ Fix: Isothermal ≠ Adiabatic. Both frequent NEET confusion.
Chapter Intelligence
Exam data and last-minute strategy
NEET Frequency
3–4 Q/year. Carnot efficiency, first law applications, rms speed ratios, Cv/Cp/γ values, and isothermal vs adiabatic distinctions.
High-Yield
η = 1−Tc/Th. v_rms ∝ 1/√M. ΔU = Q−W. Cp−Cv = R. γ = 5/3 (monatomic), 7/5 (diatomic).
Strategy
Memorise Carnot formula and the three speed formulas. Practice efficiency and speed-ratio problems — they're straightforward formula substitutions.
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