Physics notesThermalThermo
Independent topic page
Fix the sign convention and process type in 15 seconds; First-law ledger plus Carnot bound controls almost every Advanced thermo stem, including multi-process cycles.
01. Heat and work are path functions; U is a state function. First law (common Physics convention): ΔU=Q−W with W=work done by the system, or check the paper’s stated form ΔU=Q+W if W is on the system—pick one and never mix mid-solution.
02. For ideal gases, ΔU=nC_VΔT on every path. Isothermal ⇒ ΔU=0; isochoric ⇒ W=0 (P dV); isobaric ⇒ W=PΔV; adiabatic ⇒ Q=0.
03. Second law: heat engines need two reservoirs; Carnot efficiency η=1−T_C/T_H (kelvin) is the upper bound for reversible engines between those temperatures.
04. Reversible vs irreversible: same endpoints can share ΔU but differ in Q and W; irreversible adiabatic can change T differently from PV^γ reversible adiabatic.
05. Cycle work equals enclosed P–V area (orientation for sign). Advanced multi-correct often asks which quantities are state functions — U, H-like ideal-gas U(T), not Q or W.
06. Stamp the First-law sign convention once (physics: ΔU=Q−W or Q+W—pick the paper’s habit and never mix). Ideal gas: ΔU=nC_VΔT on any path between two T’s.
07. Path functions Q and W need process identity: isochoric W=0, isobaric W=PΔV, isothermal ideal ΔU=0, adiabatic Q=0. Cycles: ΣΔU=0.
08. Engines: η=W/Q_H ≤ 1−T_C/T_H with kelvin temperatures. Carnot is the reversible limit—irreversible adiabatics do not enjoy PV^γ casually.
Official · 2026
Official syllabus points for Thermodynamics only — not the full Thermal portion map. Portion hub: Thermal · Thermodynamics/Kinetic Theory analysis.
No topic-specific exclusions flagged — finish the unit points below for Thermo.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusFirst law, processes (isothermal/adiabatic), Carnot, and entropy basics.
Syllabus points
Do / check
2020–2026 paper weight
Topic match inside parent portion Thermodynamics/Kinetic Theory (11.5% of Physics tags). Stats below are portion backdrop; matched subtopics show where Thermodynamics sits.
Portion-wide type/difficulty mix lives on the Thermodynamics/Kinetic Theory analysis — not repeated here so this page stays on Thermo.
01. Thermodynamics/Kinetic Theory accounts for ~11.5% of tagged physics questions (2020–2026).
Full PCM trends board → · Thermodynamics/Kinetic Theory subject page →
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Thermodynamics — practise the knowledge bridge, not only the single-chapter drill.
No tagged mixed stem matched this topic’s keywords yet. Still revise the joins listed under Trends, and scan the mixed joins board for Mechanics / EM / Optics bridges.
Why methods matter
Path labels fix w and q; state functions fix ΔU — Advanced cycles punish silent sign flips.
Eliminates the #1 Advanced thermo arithmetic error.
Do thisWrite ‘W by’ or ‘W on’ at the top of the rough sheet before any number.
Eliminates the #1 Advanced thermo arithmetic error.
If ΔU=Q−W and isothermal ideal ΔU=0, then Q=W_by=nRT ln(V₂/V₁).
Cycles become addition, not narrative.
Do thisFor each process column: type | ΔT | ΔU | W | Q.
Cycles become addition, not narrative.
Isochoric heating: W=0, Q=ΔU=nC_VΔT; next isobaric expansion fills W=PΔV.
Instant multi-correct filter on impossible engines.
Do thisBefore trusting a claimed η, compute 1−T_C/T_H and reject anything larger.
Instant multi-correct filter on impossible engines.
T_H=400 K, T_C=300 K ⇒ η_C=25%; a claimed 40% engine is impossible.
Blocks irreversible-process traps.
Do thisCompute ΔU from endpoints only; never infer Q from ΔU alone without the path.
Blocks irreversible-process traps.
Same (P₁,V₁)→(P₂,V₂) via different paths: same ΔU, different Q,W.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
One mole ideal gas is heated isochorically so ΔT=10 K. Take C_v=1.5R. Find ΔU.
This stem rewards early recognition of the first-law process accounting model.
Model chosenΔU=nC_vΔT.
Answer15R
Takeaway: Isochoric ΔU still follows C_vΔT.
An ideal gas with γ=1.4 is compressed adiabatically from V to V/2. Find T₂/T₁.
This stem rewards early recognition of the adiabatic and polytropic relations model.
Model chosenT V^{γ−1}=const.
Answer2^{0.4}
Takeaway: Use the adiabatic invariant matching the known pair.
One mole of a monatomic ideal gas executes the cycle A→B isochoric P→2P, B→C isobaric V→2V, C→D isochoric P→P, D→A isobaric V→V. If T_A=T₀, find the efficiency.
This Advanced-level variation couples hidden constraints with the pv diagram cycle work model.
Model chosenSum Q on heat-absorbing legs only; W_net equals the PV area.
Answer2/13
Takeaway: Efficiency needs an explicit Q_in sum, not only net work.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likeIsochoric/isobaric/isothermal/adiabatic/irreversible
Fast modelLabel path; then ΔU=q+w with paper’s sign convention.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeClosed loop; efficiency or net work
Fast modelW_net = area; for ideal gas use process formulas on each leg.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeTV^{γ−1}, PV^γ, or polytropic n
Fast modelUse the matching invariant for reversible adiabatic ideal gas.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeη_Carnot, refrigerator COP, or irreversibility
Fast modelη≤1−T_C/T_H; equality only for Carnot.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline given/asked quantities, free/closed surface labels, idealisations and the exact target. Reject any formula whose assumptions are already violated.
Write the governing relation symbolically before substitution; define a control volume, free body, reference level, or thermodynamic path if the stem mixes regimes.
Keep ratios and differentials exact as long as possible. Carry signs, gauge/absolute pressures, degrees of freedom and units on the rough sheet instead of repairing them later.
Check dimensions, limiting cases and physical sense. For multi-correct, test every option independently rather than forcing one common conclusion.
After the model is locked
ΔU=Q−W (W by system) — or ΔU=Q+W (W on system); lock one
Every thermo energy balance
ΔU=n C_V ΔT (any path)
Ideal gas
W_by=∫P dV; isobaric PΔV; isothermal nRT ln(V₂/V₁)
Ideal-gas paths
W_by=(nRΔT)/(1−γ)=−ΔU (Q=0)
Reversible adiabatic ideal gas
η=W/Q_H=1−|Q_C|/Q_H
Heat engine
η_C=1−T_C/T_H (T in kelvin)
Reversible engine between two reservoirs
COP=Q_C/W=Q_C/(Q_H−Q_C)
Fridge/heat pump definitions differ—read ask
ΔU_cycle=0 ⇒ Q_net=W_net (with consistent signs)
Closed cycles
Make it automatic