L-11: Thermodynamics

Thermodynamics — Heat, Work, and Energy Flow

Thermodynamics is the phenomenological science of thermal energy transfer between bodies at different temperatures. Rubbing hands, inflating a bicycle tyre, or ice melting in warm water all involve conversion between mechanical work and thermal effects.

NIOS objectives: indicator diagrams; thermodynamic equilibrium; Zeroth law; internal energy; first law and limitations; triple point; second law; Carnot cycle and efficiency.

11.1 Concept of Heat and Temperature

11.1.1 Heat

Heat is energy transferred between two systems (or a system and surroundings) because of a temperature difference. Direction of flow is always from higher to lower temperature until thermal equilibrium is reached.

Joule showed equivalence of heat and mechanical work — molecular motion is associated with heat. Units:

• calorie (cal): heat to raise 1 g water from 14.5°C to 15.5°C
• 1 kcal = 10³ cal
• 1 cal = 4.18 J

11.1.2 Temperature

Temperature is the property that determines whether a body is in thermal equilibrium with others. All bodies in thermal equilibrium share the same temperature.

11.1.3 Thermodynamic Terms

• System: definite quantity of matter separated by a boundary (real or imaginary).
• Surroundings: everything outside the boundary.
• Open system: exchanges mass and energy.
• Closed system: exchanges energy only.
• Isolated system: exchanges neither.
• Variables: P, V, T describe the thermodynamic state.
• Indicator diagram: P–V graph showing how pressure varies with volume during a process.

Work done on the system is taken as negative; work done by the system is positive.

11.2 Thermodynamic Equilibrium and Processes

A liquid at 60°C left in a room reaches room temperature — thermal equilibrium. When unbalanced forces cease → mechanical equilibrium. When chemical reactions stop → chemical equilibrium. All three together → thermodynamic equilibrium.

11.2.1 Types of Processes

• Reversible: slow, through equilibrium states; can be retraced (melting ice ↔ refreezing; spring loading). Ideal only.
• Irreversible: cannot retrace same equilibrium path (friction, dissolving sugar, rusting). All natural processes.
• Isothermal: constant T; heat flows to/from surroundings to maintain temperature.
• Adiabatic: no heat exchange — ΔQ = 0.
• Isobaric: constant P.
• Isochoric: constant V → no expansion work.
• Cyclic: returns to initial state → ΔU = 0.

11.2.2 Zeroth Law of Thermodynamics

If systems A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other. This law provides the basis for temperature as a measurable quantity.

Phase Diagram and Triple Point

Matter exists as solid, liquid, and gas (phases). A phase diagram plots P vs T showing fusion curve (melting), vaporization curve (boiling), and sublimation (hoarfrost) curve. Where extended curves meet is the triple point — all three phases coexist.

• Latent heat of fusion: heat to convert unit mass solid → liquid at melting point.
• Latent heat of vaporization: heat to convert unit mass liquid → gas at boiling point.

Triple point of water is the upper fixed point in the Kelvin thermometric scale — uniquely stable T and P.

11.3 Internal Energy of a System

Internal energy U = kinetic energy of molecules + potential energy from intermolecular forces. For a metal: electron KE + atomic PE + lattice vibration energy.

U is a state function — depends only on state variables (P, V, T), not the path. For adiabatic work W done on system:

11.4 First Law of Thermodynamics

Conservation of energy for thermodynamic systems: heat supplied to a system equals change in internal energy plus work done by the system.

Sign conventions:

• ΔW positive when system expands (work by system).
• ΔW negative when system compressed (work on system).
• ΔQ positive when heat added to system.
• ΔU positive when internal energy increases.

ΔQ and ΔW depend on path; ΔU depends only on initial and final states.

11.4.1 Limitations

• Does not forbid heat flowing from cold to hot — fails to give direction of heat flow.
• Does not state how much heat can be converted to work — needs second law.

11.5 Second Law of Thermodynamics

Kelvin-Planck: It is impossible for any system to absorb heat from a reservoir at fixed temperature and convert all of it into work.

Clausius: It is impossible for heat to flow from a colder body to a hotter body without external work.

A heat engine needs: (i) hot source, (ii) cold sink, (iii) working substance. It absorbs H₁ from source, does work W, rejects H₂ to sink.

11.5.1 Carnot Cycle

         CARNOT CYCLE (reversible ideal engine)
         ====================================
    A ──isothermal expansion──► B   (absorb H₁ from source T₁)
    B ──adiabatic expansion───► C   (T falls to T₂)
    C ──isothermal compression► D   (reject H₂ to sink T₂)
    D ──adiabatic compression─► A   (T rises back to T₁)
                    |
                    v
         Net work W = area ABCD on P–V diagram
         ΔU = 0 for complete cycle  →  W = H₁ − H₂

11.5.2 Efficiency of Carnot Engine

Example: Source 400 K, absorbs 200 cal, rejects 150 cal → sink T₂ = 300 K, η = 25%.

11.5.3 Limitations of Carnot Engine

Isothermal steps need infinitely slow piston motion for heat transfer; adiabatic steps need infinitely fast motion to prevent heat leak. These ideal conditions cannot be met — real engines have η < Carnot η.

Quick Revision

• Heat: energy due to ΔT; 1 cal = 4.18 J.
• Work: ΔW = PΔV; area under P–V curve.
• Zeroth law: defines temperature via thermal equilibrium.
• First law: ΔQ = ΔU + ΔW; U is state function.
• Second law: Kelvin-Planck + Clausius; limits heat engines.
• Carnot: η = 1 − T₂/T₁; maximum possible efficiency.
• Triple point: solid, liquid, vapour coexist.