Part III — Thermodynamics

Chapter 3: Laws of Thermodynamics and Thermal Cycles

3.1 Basic Concepts

Thermodynamics studies energy, heat, and work, and their relationships to the properties of matter. A system is the region of interest under study; a closed system exchanges energy (heat/work) but not mass with its surroundings, while an open system exchanges both energy and mass. State variables (pressure, temperature, volume, internal energy, etc.) describe the condition of a system.

3.2 The Laws of Thermodynamics

The Zeroth Law of Thermodynamics states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other — the basis for defining temperature and temperature measurement. The First Law of Thermodynamics is a statement of energy conservation: the change in internal energy of a system equals heat added minus work done by the system (ΔU = Q − W). The Second Law of Thermodynamics establishes the direction of natural processes and the impossibility of a heat engine with 100% efficiency (some heat must always be rejected to a lower-temperature sink) — commonly stated via the Kelvin-Planck statement (no engine can convert heat completely into work in a cyclic process) or the Clausius statement (heat cannot spontaneously flow from a colder to a hotter body without external work input). The Third Law of Thermodynamics states that the entropy of a perfect crystal approaches zero as temperature approaches absolute zero.

3.3 Heat Engines and the Carnot Cycle

A heat engine converts heat energy into mechanical work, operating in a cycle between a high-temperature source and a low-temperature sink. The Carnot cycle, an idealised, reversible cycle, represents the theoretical maximum possible efficiency for any heat engine operating between two given temperatures, with efficiency η = 1 − (T_L/T_H), where T_L and T_H are the absolute (Kelvin) temperatures of the sink and source respectively — no real engine can exceed this Carnot efficiency for the same temperature limits.

3.4 Practical Thermodynamic Cycles

The Otto cycle is the idealised air-standard cycle for spark-ignition (petrol) engines, with heat addition occurring at constant volume. The Diesel cycle is the idealised air-standard cycle for compression-ignition (diesel) engines, with heat addition occurring at constant pressure. The Rankine cycle is the idealised cycle used to model steam power plants, involving a boiler (constant-pressure heat addition), turbine (isentropic expansion), condenser (constant-pressure heat rejection), and feed pump (isentropic compression).

3.5 Practice Set — Thermodynamics (16 MCQs)

1. The Zeroth Law of Thermodynamics forms the basis for defining:
   (a) Pressure (b) Temperature (c) Volume (d) Density
2. The First Law of Thermodynamics is fundamentally a statement of:
   (a) Entropy increase (b) Energy conservation (c) Temperature equilibrium (d) Zero absolute temperature
3. The First Law of Thermodynamics is expressed as:
   (a) ΔU = Q − W (b) ΔU = Q + W (c) ΔU = Q × W (d) ΔU = W − Q
4. The Kelvin-Planck statement of the Second Law asserts that:
   (a) No engine can convert heat completely into work in a cyclic process (b) All engines are 100% efficient (c) Heat always flows from cold to hot spontaneously (d) Entropy always decreases
5. The Clausius statement of the Second Law asserts that:
   (a) Heat cannot spontaneously flow from a colder to a hotter body without external work (b) Heat always flows from cold to hot spontaneously (c) All processes are reversible (d) Entropy is always zero
6. The Third Law of Thermodynamics concerns the behaviour of entropy as temperature approaches:
   (a) Infinity (b) Absolute zero (c) Room temperature (d) The boiling point of water
7. A closed thermodynamic system exchanges with its surroundings:
   (a) Both mass and energy (b) Energy but not mass (c) Mass but not energy (d) Neither mass nor energy
8. An open thermodynamic system exchanges with its surroundings:
   (a) Both mass and energy (b) Energy but not mass (c) Mass but not energy (d) Neither mass nor energy
9. The Carnot cycle efficiency formula is:
   (a) η = 1 − (T_L/T_H) (b) η = T_L/T_H (c) η = T_H/T_L (d) η = 1 + (T_L/T_H)
10. The Carnot cycle represents:
    (a) The minimum possible efficiency for a heat engine (b) The theoretical maximum possible efficiency for a heat engine between two given temperatures (c) An efficiency independent of temperature (d) A cycle used only in refrigeration
11. The Otto cycle is the idealised air-standard cycle for:
    (a) Compression-ignition (diesel) engines (b) Spark-ignition (petrol) engines (c) Steam power plants (d) Gas turbines exclusively
12. In the Otto cycle, heat addition occurs at constant:
    (a) Pressure (b) Volume (c) Temperature (d) Entropy only
13. The Diesel cycle is the idealised air-standard cycle for:
    (a) Spark-ignition (petrol) engines (b) Compression-ignition (diesel) engines (c) Steam power plants (d) Refrigeration cycles
14. In the Diesel cycle, heat addition occurs at constant:
    (a) Volume (b) Pressure (c) Entropy only (d) Temperature
15. The Rankine cycle is the idealised cycle used to model:
    (a) Petrol engines (b) Diesel engines (c) Steam power plants (d) Refrigeration systems only
16. The Rankine cycle's main components include a boiler, turbine, condenser, and:
    (a) Feed pump (b) Carburettor (c) Spark plug (d) Piston-cylinder assembly only

Answer Key

1.(b)

2.(b)

3.(a)

4.(a)

5.(a)

6.(b)

7.(b)

8.(a)

9.(a)

10.(b)

11.(b)

12.(b)

13.(b)

14.(b)

15.(c) 16.(a)