Thermodynamics - Class 11 Physics

Thermodynamics

Overview: Study of interconversion of heat and other forms of energy. Macroscopic view.

1. Laws of Thermodynamics

Zeroth Law

If A and B are in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. (Concept of Temperature).

First Law

Conservation of Energy. Energy supplied = Work done + Internal Energy change.

ΔQ = ΔU + ΔW

Sign convention: Heat gained +ve, Work by system +ve.

Second Law

Kelvin-Planck: Impossible to build an engine with 100% efficiency. Source and Sink both required.

Clausius: Heat cannot flow from cold to hot body without external work.

2. Thermodynamic Processes

Isobaric Process

Pressure constant. W = P(V2 - V1).

Isochoric Process

Volume constant. W = 0.

Isothermal Process

Temperature constant. PV = constant. ΔU = 0.

W = nRT ln(V₂/V₁)

Adiabatic Process

No heat exchange (ΔQ = 0). PV^γ = constant.

W = (P₁V₁ - P₂V₂) / (γ - 1)

3. Heat Engines & Refrigerators

Efficiency (η)

Ratio of Work output to Heat input.

η = W / Q₁ = 1 - Q₂/Q₁

Carnot Engine

Ideal reversible engine. Maximum possible efficiency.

η = 1 - T₂/T₁

Refrigerator (Coefficient of Performance β)

Ratios Heat extracted to Work done.

β = Q₂ / W = T₂ / (T₁ - T₂)

Numericals - Thermodynamics

Numericals

First Law

Q1. Heat supplied is 100J. Work done by system is 40J. Change in Internal Energy?

ΔQ = ΔU + ΔW

100 = ΔU + 40

ΔU = 60 J

Carnot Efficiency

Q2. Carnot engine operates between 227°C and 27°C. Find efficiency.

Convert to Kelvin: T1 = 227+273 = 500K

T2 = 27+273 = 300K

η = 1 - T2/T1

η = 1 - 300/500 = 1 - 0.6 = 0.4

Efficiency = 40%

Refrigerator COP

Q3. Freezer at -10°C. Room at 30°C. COP?

T2 = 263K, T1 = 303K

β = T2 / (T1 - T2)

β = 263 / (303 - 263)

β = 263 / 40 ≈ 6.57

Isobaric Work

Q4. Gas expands from 2L to 6L at constant P=10⁵ Pa. Work Done?

W = P(V2 - V1)

W = 10⁵ (6 - 2) × 10^-3

W = 10⁵ × 4 × 10^-3

W = 400 J

Adiabatic Process

Q5. Gas compressed adiabatically to half volume. Ratio of final pressure to initial? (γ=1.4)

P1 V1^γ = P2 V2^γ

P2/P1 = (V1/V2)^γ

Ratio = (2)^1.4 ≈ 2.64

Pressure increases 2.64 times.

Isothermal Work

Q6. 1 mole of gas expands isothermally from V to 2V at 300K. Work? (R=8.3)

W = 2.303 RT log(V2/V1)

W = 2.303 × 8.3 × 300 × log(2)

W = 2.303 × 2490 × 0.301

W ≈ 1726 J

Cyclic Process

Q7. In cyclic process, ΔQ = 50J. What is Work done?

For cyclic process, ΔU = 0.

ΔQ = ΔW

Work = 50 J

Cp Cv Application

Q8. For monoatomic gas, ratio Cp/Cv?

γ = 1 + 2/f

f = 3 (monoatomic)

γ = 1 + 2/3 = 5/3 = 1.67

Internal Energy

Q9. Ideal gas internal energy depends on?

Depends only on Temperature.

U = f/2 nRT

(Conceptual numerical)

Engine Work

Q10. Engine absorbs 1000J and rejects 600J per cycle. Power output if 10 cycles/sec?

Work per cycle = Q1 - Q2 = 1000 - 600 = 400 J

Power = Work/time = Work × frequency

P = 400 × 10 = 4000 Watts = 4 kW

Formulas & Facts - Thermodynamics

Equations & Formulas

Concept	Formula
First Law	ΔQ = ΔU + ΔW
Work (Isobaric)	P(V₂ - V₁)
Work (Isothermal)	nRT ln(V₂/V₁)
Work (Adiabatic)	(P₁V₁ - P₂V₂)/(γ-1)
Adiabatic Relation	TV^γ-1 = Const
Efficiency	η = 1 - Q₂/Q₁
Carnot Eff	η = 1 - T₂/T₁
COP (Fridge)	β = T₂ / (T₁ - T₂)
Mayer's Relation	C_p - C_v = R

50 NEET Facts

Key points for Thermodynamics.

1. System & Surroundings Everything outside system is surroundings. Universe = System + Surroundings.

2. Open System Exchanges both Energy and Matter.

3. Closed System Exchanges Energy but not Matter.

4. Isolated System Exchanges neither Energy nor Matter.

5. Zeroth Law Defines Temperature. Basis of thermometers.

6. Internal Energy (U) State function. Depends only on T for ideal gas. Sum of KE and PE of molecules.

7. Isothermal Process Slow process. Container must be conducting. T constant.

8. Adiabatic Process Fast process (Bursting tire). Insulated container. Q constant.

9. Slope of PV Graph Adiabatic slope (γ times) > Isothermal slope.

10. Work in Expansion Positive. Work done BY gas.

11. Work in Compression Negative. Work done ON gas.

12. Cyclic Process Initial and Final states same. ΔU = 0. ΔQ = ΔW.

13. Area under PV Curve Gives Work done.

14. Area inside Cycle Net work done per cycle. Clockwise = +ve work (Engine). Anticlockwise = -ve work (Fridge).

15. Free Expansion Expansion in vacuum. P_ext = 0. W = 0, Q = 0, ΔU = 0, ΔT = 0.

16. Second Law Significance Direction of heat flow and limit of efficiency.

17. Heat Engine Converts Heat to Work. High T Source -> W -> Low T Sink.

18. Efficiency Limit Always < 100%. (Unless Sink is at 0K, which is impossible).

19. Refrigerator Heat Pump. Work done to extract heat from Cold body to Hot body.

20. Open Fridge Room If fridge door is left open, room warms up (Work done adds heat).

21. Reversible Process Quasi-static, no friction. Idealized.

22. Irreversible Process Real processes (friction, fast expansion). Entropy increases.

23. Carnot Cycle 2 Isothermals + 2 Adiabatics. Most efficient.

24. Efficiency Dependency Depends only on source and sink temperatures (T1, T2).

25. CP > CV At constant P, heat does work + raises temp. At constant V, heat only raises temp.

26. Gamma (γ) CP/CV. Mono=1.67, Di=1.4, Poly=1.33.

27. Degrees of Freedom (f) Mono=3, Di=5 (at low T), 7 (high T).

28. Relation Cv & f Cv = f/2 R.

29. Relation Cp & f Cp = (1 + f/2) R.

30. Mixing of Gases Internal energy adds up. U_mix = U1 + U2.

31. Order of Motion Heat is random motion. Work is organized motion. Work -> Heat easy. Heat -> Work difficult.

32. Triple Point of Water Unique point. Used to define Kelvin scale.

33. P-T Graph Slope Isochoric line slope depends on Volume.

34. V-T Graph Slope Isobaric line slope depends on Pressure.

35. Entropy (S) Measure of disorder. ΔS = ΔQ/T.

36. 3rd Law Entropy of perfect crystal at 0K is zero.

37. Cooling by Adiabatic Exp Rapid expansion causes cooling (Gas does work at cost of internal energy).

38. Diesel Engine No spark plug. Ignites by compression (Adiabatic heating).

39. Steam Engine Rankine cycle. External combustion.

40. Petrol Engine Otto cycle. Internal combustion.

41. Efficiency 100% Only if T_sink = 0 K (Impossible).

42. Perpetual Motion Machine 1 Violates 1st Law (Creators energy). Impossible.

43. Perpetual Motion Machine 2 Violates 2nd Law (100% efficiency). Impossible.

44. Melting Process Isothermal and Isobaric. ΔU > 0, ΔS > 0.

45. Boiling Process Isothermal and Isobaric. Huge volume change.

46. Sound Propagation Adiabatic process in air.

47. Heat Death Universe tending towards max entropy and constant temp.

48. Extensive Properties Depend on mass (U, V, S, H).

49. Intensive Properties Independent of mass (P, T, Density).

50. Path Functions Work and Heat. Value depends on path taken.

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