First Law of Thermodynamics

• The First Law: ΔU = Q − W — conservation of energy for thermodynamic systems.
• Sign conventions for heat Q and work W in physics (system-centric).
• Isothermal, isobaric, isochoric, and adiabatic processes for ideal gases.
• To calculate work as area under P–V diagram and apply to engines and compressors.

Level 1 — Energy balance

Verbal: Internal energy U changes when heat enters/leaves the system and when the system does work on surroundings (or vice versa). Energy is conserved; it transforms between heat, work, and internal energy.

Symbolic: ΔU = Q − W (common NCERT convention: W = work done by system). If heat added to system, Q > 0. If system expands against external pressure, W > 0.

For ideal gas: U depends only on T (for fixed n). Isothermal ⇒ ΔU = 0 ⇒ Q = W.

Level 2 — Processes and formulas (ideal gas)

Mayer relation: C_P − C_V = R (1 mole ideal gas). γ = C_P/C_V.

P–V diagram: Work = ∫P dV = area under curve (signed).

Cyclic process: ΔU = 0 ⇒ Q_net = W_net (area enclosed).

NCERT spotlight — Cyclic processes and engines

In a cyclic process Delta U = 0, so Q_net = W_net equals area enclosed on P-V diagram. Heat engine absorbs Q_h, rejects Q_c, work W = Q_h - Q_c. Efficiency eta = W/Q_h = 1 - Q_c/Q_h.

Adiabatic relations (ideal gas): PV raised to gamma equals constant, TV raised to (gamma-1) equals constant during reversible adiabatic process — used in sound propagation and compression strokes.

Calorimetry: Q = mc Delta T for sensible heating; Q = mL for phase change at constant temperature.

One mole of ideal gas expands isothermally at 300 K from 2 L to 8 L. Find W and Q (R = 8.314 J/mol·K).

Step 1 — Isothermal ideal gas: ΔU = 0 → Q = W.
Step 2 — W = nRT ln(V₂/V₁) = 1 × 8.314 × 300 × ln(8/2).
Step 3 — ln 4 = 1.386 → W = 8.314 × 300 × 1.386 ≈ 3457 J.
Step 4 — Q = +3457 J (heat absorbed from reservoir to do expansion work).
Step 5 — Temperature constant: internal energy of ideal gas unchanged ✓

Applications — engines and compressors

Petrol engine approximate Otto cycle: intake, compression, ignition, exhaust — net work per cycle equals area on P-V loop. Refrigerator removes heat Q_c from cold space using work W; COP_refrigerator = Q_c/W. First law tracks where energy goes: not created, only transformed among heat, work, and internal energy.

Deep dive — cyclic processes and heat capacities

Cyclic process ΔU = 0 ⇒ Q_net = W_net = area enclosed clockwise on P-V diagram work positive by system if clockwise convention standard thermodynamics. Two moles ideal gas heated isochorically: Q = n C_V ΔT = 2 × (3/2 R) ΔT for monatomic — C_V = (3/2)R monatomic, (5/2)R diatomic at moderate T. ** Mayer relation** C_P − C_V = R derives from enthalpy H = U + PV for ideal gas. Polytropic process PV^n = constant — generalises isobaric isothermal adiabatic (n=gamma). Free expansion into vacuum Q=0 W=0 ΔU=0 ideal gas but irreversible entropy increases. Calorimeter mixing hot cold water: m1 c (T_f − T1) + m2 c (T_f − T2) = 0 find T_f — first law calorimetry special case no work. Adiabatic sound speed related gamma — physics acoustics link. Practise P-V diagram sketching for each process direction — examiners test area sign conventions frequently in CBSE 3-mark questions.

Review and practice drill

Review checklist: (1) Delta U = Q - W sign convention NCERT. (2) Isothermal ideal gas Delta U = 0. (3) Work = area P-V diagram. (4) Adiabatic Q = 0 so Delta U = -W. Practice: Gas absorbs 500 J, does 200 J work — Delta U = 300 J.

• A gas absorbs 500 J heat and does 200 J work. Find ΔU.
• Why is work zero in isochoric heating?
• Sketch isobaric expansion on P–V diagram and identify work area.

Open the Practice tab for graded questions on First Law.

• Use the platform-native live simulation or PhET-style tool for this topic (number line, Venn, physics playground, molecule builder, sensor dashboard, etc.).
• Mirror / body / home activity: physically do the concept (count objects, measure, role-play) and photograph or describe for portfolio.
• Voice or text reflection with AI Mentor: explain the concept to a younger student or family member.

• "Explain this concept to a Class 6 student using one real example from an Indian home, school, market, or festival."
• "What is one common mistake students make here, and how would you catch yourself making it?"
• Stretch: "How does this connect to coding, robotics, money, health, environment, or a future career?"

• Complete the core practice + one extension activity (photo, table, short reflection, or mini-project) for base XP + topic badge.
• 5-7 day streak or family discussion note = multiplier + visible artifact in parent/principal dashboard.
• Best real-world application stories (anonymised) featured on class or national leaderboard.

• One hands-on project or measurement using the Drishti kit or household items that makes the concept physical.
• Direct link to at least one Future Skill track (Money Management, Green Tech, Cyber Defenders, Micro-Entrepreneurship, AI Mastery, Sustainable Living, Personality Development).
• Coding extension where relevant (simple script, simulation, or data logging).

This material emphasises experiential "learning by doing", competency (apply/create/analyse), vocational exposure, critical thinking, and multidisciplinary connections. Designed to feed live worlds, AI Mentor (with memory), gamification, robotics, parent analytics, and future skills — not just exam prep.

Portfolio Evidence Idea: Your photo/table/reflection/project + one sentence on "How this helps me in real life or a possible future path."

Open the Practice tab for aligned questions (easy/medium/hard + case-based) with full AI scaffolding.

See curriculum for cross-links and the full future-skills/robotics chapters.