Temasek Physics 6091 Notes: Thermal Physics to Electromagnetism

Thermal Physics

Kinetic Particle Model of Matter
- Solids: molecules vibrate about fixed positions; held by strong intermolecular bonds; fixed volumes and shapes; high densities due to close packing.
- Liquids: molecules move freely within a vessel; held by strong intermolecular bonds; fixed volume but take the shape of their container; molecules randomly arranged with particles slightly further apart; relatively high densities.
- Gases: molecules have weak intermolecular bonds and move randomly at very high speeds; no fixed shape or volume and are highly compressible; molecules are very far apart and randomly arranged; very low densities.
Brownian Motion
- Continuous random motion of fluid molecules; evidence for the kinetic model of matter.
- Uneven bombardment of particles by molecules causes unbalanced forces, leading to erratic motion.
Pressure of a Gas
- Pressure is due to bombardment of gas molecules on container walls; depends on rate and speed of collisions (P ∝ frequency and mean impact force).
Temperature of a Gas
- The average kinetic energy of gas molecules depends on temperature; as temperature rises, thermal energy increases and is converted to kinetic energy, so molecules move faster.
Gas Laws and Kinetic Theory (names not required)
- Constant Volume: $P \nabla T \, (\text{at constant } V)$
- Constant Pressure: $V \nabla T \, (\text{at constant } P)$
- Constant Temperature: $P \propto \frac{1}{V} \, (\text{ Boyle's Law})$
- Common forms:
- Pressure proportional to temperature at constant volume: $P \propto T \, (\text{constant } V)$
- Volume proportional to temperature at constant pressure: $V \propto T \, (\text{constant } P)$
- Inverse relation between pressure and volume at constant temperature: $P1 V1 = P2 V2$
Thermal Equilibrium and Heat Transfer
- Thermal Equilibrium: when two bodies in contact have no net heat transfer, they are at the same temperature.
- Heat Transfer: from hotter to cooler object when a temperature difference exists.
- Conduction (solids): main mode of heat transfer in solids.
- Mechanisms:
  1) Lattice/molecular vibration: transfer of vibrational KE between fixed lattice sites.
  2) Free electron diffusion (predominant in metals): free electrons gain energy and transfer energy upon collisions.
- Solids are better conductors than liquids; gases are poor conductors.
- Convection (fluids): heat transfer via movement of heated fluid; main mode within liquids/gases; mechanism: bulk movement due to density changes; heated fluid expands, density decreases, so it rises; cooler fluid sinks, forming convection currents; more readily in gases than in liquids.
- Radiation: energy transfer by electromagnetic waves; can occur in vacuum; good radiators are good absorbers and poor reflectors.
Applications of Thermal Energy Transfer
- Vacuum Flask: double-walled bottle with silvered surfaces to reflect radiation; stopper as insulator; vacuum between walls to prevent conduction; prevents convection and evaporation.
Internal Energy and Specific Heat
- Internal energy: total internal kinetic energy of random motion plus total potential energy between particles.
- Specific heat capacity (per unit mass): $Q = mc\Delta\theta$ where $Q$ is the heat added, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta\theta$ is the change in temperature.
- Heat capacity of an object: $Q = C \Delta\theta$ where $C$ is the heat capacity of the object.
Latent Heat and Changes of State
- Latent heat of fusion (Lf): energy required to change solid to liquid at constant temperature.
- Latent heat of vaporization (Lv): energy required to change liquid to gas at constant temperature.
- Latent heat (L) for a phase change is energy absorbed or released to change the state, increasing potential energy (intermolecular distance) with average kinetic energy remaining constant during the phase change. Hence $Lf < Lv$ .
- Specific latent heats:
- $Q (Lf) = m \cdot L_f$ where $m$ is mass.
- $Q (Lv) = m \cdot L_v$
Phase Changes
- Melting: solid to liquid; latent heat used to break intermolecular bonds; potential energy increases; kinetic energy remains constant.
- Freezing/Condensation: molecules lose potential energy; bonds form; potential energy decreases; kinetic energy remains constant.
- Boiling and Condensation: Boiling transfers energy to change state from liquid to gas at constant temperature; condensation is the reverse.
Melting and Boiling Compared to Evaporation
- Melting: solid to liquid at constant temperature; no temp change during the phase change.
- Boiling: liquid to gas at fixed temperature; requires larger energy than melting due to larger intermolecular distance and doing work against atmospheric pressure; evaporation occurs at the surface at any temperature and cools the liquid as high-energy molecules escape.
Heating Curve Interpretation
- When temperature rises, energy goes into increasing kinetic energy (temperature rise).
- During a phase change, added energy increases internal potential energy (changes in intermolecular distance); temperature remains constant.

Electricity and Magnetism

Electric Charge and Electrostatics
- Charges are measured in coulombs (C).
- The charge on one electron is $-1.6 \times 10^{-19} \text{ C}$ .
- Two types of charges: positive and negative.
- Law of electrostatics: unlike charges attract; like charges repel.
Electric Field and Lines of Force
- Electric field is a region where a charge experiences a force.
- The direction of the field is the direction of the force on a positive test charge.
- An electric line of force is the path a positive charge would take if free to move.
Static Electricity Experiments and Concepts
- Charging by induction: charging conductors without direct contact; involves bringing a charged body near a conductor and grounding to allow charge transfer.
- Charging by friction (by rubbing) transfers electrons; results in charge separation.
- Insulators vs Conductors: insulators resist charge flow; conductors allow charge flow.
- Applications: photocopiers, laser printers, electrostatic paint spraying, electrostatic precipitators.
- Hazards: discharge of static charges can cause sparks and fires if flammable materials are present.
Current of Electricity
- Current (I): rate of flow of charge; unit ampere (A).
- Relationship: $I = \frac{Q}{t}$ where $Q$ is charge in coulombs and $t$ is time in seconds.
- Measuring current: ammeter must be connected in series in the circuit.
Electromotive Force (EMF) and Potential Difference
- EMF ((\mathcal{E})) is the work done by the source in driving a unit charge around a complete circuit: $\mathcal{E} = \frac{W}{Q}$ with units J/C or volts (V).
- Series: total EMF equals the sum: $\mathcal{E}{\text{tot}} = \mathcal{E}1 + \mathcal{E}2 + \mathcal{E}3 + \cdots$
- Parallel: EMF is the same across each source: $\mathcal{E}{\text{tot}} = \mathcal{E}1 = \mathcal{E}2 = \mathcal{E}3 = \cdots$
- Potential Difference (PD): work per unit charge across a component; measured by voltmeter connected in parallel to the component.
Resistance and Ohm's Law
- Resistance: $R = \frac{V}{I}$ where $V$ is potential difference and $I$ is current.
- Temperature effect: higher temperature increases resistance in a metal conductor because lattice vibrations increase electron collisions.
- Parameters: $\rho$ (resistivity), $l$ (length), $A$ (cross-sectional area); $R = \rho \frac{l}{A}$
- Ohm's Law: current is proportional to voltage at constant temperature: $I \propto V \Rightarrow V = IR$
- IV characteristics: ohmic conductors deliver straight-line graphs; non-ohmic conductors have curved graphs.
Diode and Filament Lamp
- Diode: large current flows only when the potential difference is in the correct direction (forward bias).
- Filament lamp: resistance increases as I/V decreases (non-ohmic).
Components: Series and Parallel Circuits
- Series: Reff = R1 + R2 + R3 + … ; I = I1 = I2 = I3 = … ; V = V1 + V2 + V3 + …
- Parallel: V = V1 = V2 = V3 = … ; I = I1 + I2 + I3 + …
- In a series circuit, all components carry the same current; the largest resistance drops the largest share of the total PD.
- In a parallel circuit, the PD across all components is the same; total current is the sum of branch currents; the smallest resistance carries the greatest current.
Practical Components: Temperature-Dependent and Light-Dependent
- NTC Thermistor: resistance decreases as temperature increases.
- Light-Dependent Resistor (LDR): resistance decreases with increasing light; high in dark, low in bright light.
Unit 9: Electrical Power and Energy (DC circuits)
- Power: $P = VI = I^2 R = \frac{V^2}{R}$
- Electrical Energy: $E = Pt$ where $P$ is power and $t$ is time; or $E = VI t$ or $E = I^2 Rt$ .
- Energy cost: $E = Pt\;\text{(in kWh for billing)}; 1\;\text{kWh} = 3.6\;\text{MJ}$
Renewable and Non-renewable Energy
- Renewable energy: energy from sources that can be replenished naturally (e.g., biofuel, hydro, geothermal, wind).
- Non-renewable energy: energy from sources that cannot be replenished quickly (e.g., fossil fuels, nuclear).
Electrical Safety and Wiring (AC mains)
- Live wire (brown): ~240 V; Neutral (blue): 0 V; Earth (green/yellow): low resistance to earth.
- Switches, fuses, circuit breakers are wired to live wire.
- Fuse purpose: melts a thin wire when excessive current flows, disconnecting the circuit.
- Earth wire: provides a safe path to earth to prevent shock in case of leakage.

Magnetism and Electromagnetism

Magnetic vs Non-magnetic Materials
- Magnetic materials include iron, nickel, cobalt, steel; others are non-magnetic.
- Not all magnetic materials are magnets; magnetization must occur to become a magnet.
Induced Magnetism
- Can occur when a magnetic material is near a strong magnet or inside a current-carrying solenoid.
- Temporary magnets (soft magnetic materials, easily magnetized/demagnetized) vs Permanent magnets (hard magnetic materials, difficult to magnetize/demagnetize).
Magnetisation of Steel
- Steel bar becomes strongly magnetized when placed in a DC current through a solenoid; direction of magnetization follows the coil's N-S orientation.
Demagnetisation
- Demagnetization can occur via AC in a solenoid; heating; dropping or hammering; time causes natural demagnetization.
- Iron keepers can preserve magnet strength and prevent stray fields.
Magnetic Field Concept
- Magnetic field: region where magnetic forces act; field lines show direction of force on a north-to-south polarity; lines do not intersect.
- Field lines can be plotted with compass needles to visualize the field.
Uses of Magnets
- Temporary magnets: iron-based elements used in electromagnets for devices (doorbells, circuit breakers).
- Permanent magnets: steel-based used in DC motors, fridge doors, etc.

Electromagnetism

Magnetic Field due to Current
- Straight wire: use Right-Hand Rule (RHR, RHGR in notes) to determine B-field direction around a straight current-carrying wire.
- Circular field around a straight wire: magnitude decreases with distance and with lower current.
Magnetic Field due to a Solenoid
- Use Right-Hand Grip Rule (RHGR) to determine field direction inside a solenoid.
- In the middle of a solenoid, the magnetic field is approximately uniform; stronger with more turns, greater current, and a soft iron core.
Applications of Electromagnetism
- Electric bell: current-driven electromagnet attracts an armature to strike a bell, breaking the circuit and repeating.
- Circuit breaker: safety device that switches off current when excessive; electromagnet can attract a contact to break the circuit.
- Role of a soft-iron core: increases magnetic field strength in an electromagnet.
Fleming’s Left-Hand Rule (Motor Rule)
- Determines the direction of force on a current-carrying conductor in a magnetic field.
Force on a Current-Carrying Conductor
- A conductor in a magnetic field experiences a force when at an angle to the field; magnitude related to current and field strength.
Forces on Parallel Wires
- Parallel currents in the same direction attract; opposite directions repel.
DC Motor Details
- Closed circuit through a rectangular coil in a magnetic field results in rotation due to magnetic forces on coil arms.
- Split-ring commutator reverses current every half turn to keep rotation in the same direction.
- Increasing turns, current, or adding a soft-iron core increases turning effect.
Time-Variation and Induced Emf
- Electromagnetic induction: changing magnetic flux through a conductor induces EMF and possibly current.
- Faraday’s Law: the induced EMF is proportional to the rate of change of magnetic flux linking the circuit: $\mathcal{E} \propto \frac{d\Phi}{dt}$
- Lenz’s Law: the direction of the induced current is such that its magnetic effect opposes the change that produced it.
- Fleming’s Right-Hand Rule (Generator Rule): direction of induced current can be deduced from the relative motion of a conductor and magnetic field.

AC Generators, Transformers, and Power Transmission

AC Generator
- Structure similar to DC motor but uses slip rings to provide alternating current; coil rotation relative to magnetic field determines EMF.
- When coil is horizontal, the rate of cutting magnetic flux is maximum; EMF is maximum; when coil is vertical, rate is minimum; EMF is minimum.
- Frequency increases with rotation speed; maximum output voltage also increases with speed.
- Slip rings allow connection of the rotating coil to the external circuit without twisting wires.
Transformer Principles
- Transformers change AC voltage using mutual induction through an iron core.
- Primary coil (Np turns) and secondary coil (Ns turns) link via the iron core; changing magnetic flux induces EMF in the secondary.
- Ideal transformer relationships:
- $\frac{Vp}{Vs} = \frac{Np}{Ns}$
- $\frac{Ip}{Is} = \frac{Ns}{Np}$
- Power conservation in the ideal case: $Vp Ip = Vs Is$
- High voltage transmission benefits: high voltage with lower current reduces I^2R losses in cables.

Practical Notes and Examples

Ohm’s Law Experiment (Practical):
- Setup a resistor with a rheostat, measure current I and voltage V for different settings.
- Plot I against V; linear relationship confirms Ohm’s Law.
Determining Resistance with an Ammeter/Voltmeter
- Connect resistor with ammeter in series and voltmeter in parallel as shown; record I and V for multiple settings.
- Graph V against I (or I against V); slope or gradient yields resistance: for V vs I, R = V/I; for I vs V, R = 1/(gradient).
Magnetizing Steel with a Solenoid
- Place steel rod inside solenoid powered by DC supply; magnetization occurs as current flows.
- Confirm magnetization by demonstrating attraction of iron paper clips (or repulsion of a permanent magnet).
Verifying V Proportional to Length in a Uniform Wire
- Set up a 1 m nichrome wire AB with a voltmeter across a movable contact; vary the contact position to adjust length d.
- Record V for various d; plot V vs d; a straight line through the origin confirms direct proportionality.
Induced EMF Opposing Change (Lenz’s Law)
- Experimental setup with magnets moving through a coil showing induced EMF with a direction that opposes the change in magnetic flux.
- Demonstrates that induced EMF tends to oppose the change (e.g., opposing the approaching or receding magnet).
Fuse Blowing at a Given Current
- Circuit with rheostat set high; gradually reduce resistance while monitoring current; fuse blows when current reaches rated value (e.g., 5 A).
Force on a Current-Carrying Conductor (Magnetic Field Interaction)
- A brass rod AB placed in a magnetic field between N-S poles; current direction determines force direction; reversing current reverses force.
Thermistor and LDR Experiments
- Thermistor: resistance changes with temperature; NTC thermistors decrease resistance as temperature rises.
- LDR: resistance changes with light level; in dark, resistance is high; in bright light, resistance is low.
Applications: Electric Power and Bulb Comparisons
- Example: brightness comparisons using resistors in circuits with 240 V supply and various bulb resistances; compute currents with Ohm’s Law and compare actual power vs rated power.
- Power calculations: Power = VI = I^2R = V^2/R; actual brightness correlates with real power dissipation in each bulb.

Glossary of Terms Used in Physics Papers (Key Exam Guides)

Define: literal or equivalent formal statement; may include a defining equation.
Explain/What is meant by: include definition and significance or context.
State: concise answer, often numerical.
List: provide a number of points without elaboration.
Describe: main points with diagrams where appropriate; include observations.
Discuss: critical account of the points involved.
Outline: give essentials briefly.
Predict/Deduce: logical connections beyond direct recall.
Suggest: may have more than one valid answer or require applying general knowledge to novel situations.
Calculate: numerical answer; show working.
Measure: quantity that can be directly measured.
Determine: quantity inferred by calculation from other values.
Show: algebraic deduction to prove an equation.
Estimate: order-of-magnitude reasoning.
Sketch (Graphs/Diagrams): qualitative correctness; axes labels must be clear.
Additional: ensure proportionality and proportions are clearly indicated.

Special Notes on Formulas and Notation

All mathematical expressions are in LaTeX syntax, enclosed in double dollar signs:
- Example: $Q = mc\Delta\theta$
- Example: $P = VI = I^2R = \frac{V^2}{R}$
- Example: $R = \rho \frac{l}{A}$
- Example: $\frac{Vp}{Vs} = \frac{Np}{Ns}, \quad \frac{Ip}{Is} = \frac{Ns}{Np}, \quad Vp Ip = Vs Is$
- Example: $\mathcal{E} = -N \frac{d\Phi}{dt}$
- Example: $\frac{Vp}{Vs} = \frac{Np}{Ns}$
- Example: $E = Pt$ or $E = VI t$

Summary Connections and Real-World Relevance

The kinetic model links microscopic molecular motion to macroscopic observables like pressure, temperature, and phase changes; explains why materials behave as they do under heating and cooling.
Thermal processes underpin everyday equipment like vacuum flasks and insulation; understanding conduction, convection, and radiation helps optimize energy efficiency.
Electric circuits and magnetism form the basis of almost all electrical technology, from simple circuits to motors, generators, and transformers used in power distribution.
Practical experiments bridge theory and real-world measurements, teaching how to design, interpret, and validate physical laws (Ohm's law, electromagnetic induction, transformer action).
Safety and environmental considerations (fuse ratings, high-voltage connections, renewable vs non-renewable energy) are essential for responsible engineering and engineering ethics.