Radionuclide Imaging and Therapy (AQA A-Level Physics): Revision Notes

Definitions

1. Adiabatic Process

• Definition: A process where no heat enters or leaves the system. All changes in energy are due to work done on or by the gas.
• Explanation: In adiabatic conditions, any work done results in a change in internal energy, typically causing temperature changes within the gas.

2. Angular Acceleration

• Definition: The rate of change of angular velocity over time, measured in radians per second squared (rad/s²). It is a vector quantity.
• Formula: $\alpha = \frac{\Delta \omega}{\Delta t}$, where $\alpha$ is angular acceleration, and $\omega$ is angular velocity.

3. Angular Displacement

• Definition: The angle in radians through which an object rotates from its initial position.
• Explanation: Angular displacement indicates how far an object has rotated and is measured in radians.

4. Angular Impulse

• Definition: The product of torque and time during which the torque acts, causing a change in angular momentum.
• Formula: Angular Impulse = Torque × Time
• Explanation: Angular impulse changes an object's angular momentum, analogous to linear impulse affecting linear momentum.

5. Angular Momentum

• Definition: The product of an object's moment of inertia and angular velocity, representing the rotational equivalent of linear momentum.
• Formula: $L = I \omega$, where $I$ is the moment of inertia and $\omega$ is angular velocity.
• Explanation: Angular momentum is conserved in isolated systems with no external torque.

6. Angular Speed

• Definition: The rate at which an object rotates, measured in radians per second (rad/s). Angular speed is a scalar quantity.

7. Angular Velocity

• Definition: The rate of change of angular displacement, measured in radians per second (rad/s). It is a vector quantity.
• Formula: $\omega = \frac{\Delta \theta}{\Delta t}$, where $\theta$ is angular displacement.
• Explanation: Angular velocity indicates how quickly an object is rotating and in which direction.

8. Brake Power

• Definition: The usable power output at an engine's output shaft, accounting for power losses due to friction.
• Explanation: Brake power is the actual power available for work after internal losses are considered, making it a practical measure of engine performance.

9. Coefficient of Performance

• Definition: A measure of an engine or device's efficiency in converting work into heat transfer.
• Explanation: High coefficients of performance indicate efficient systems, particularly in heat pumps or refrigerators, where values greater than 1 are possible.

10. Conservation of Angular Momentum

• Definition: Angular momentum remains constant in a closed system with no external torque.
• Explanation: This principle explains why an ice skater spins faster when pulling in their arms, reducing moment of inertia while conserving angular momentum.

11. Constant Volume Reaction

• Definition: A reaction where the volume remains constant, so no work is done on or by the gas.
• Explanation: Any heat added to the system changes internal energy and temperature, as seen in reactions within sealed containers.

12. First Law of Thermodynamics

• Definition: States that total energy change in a system equals the work done plus the heat added or removed.
• Formula: $\Delta U = Q - W$
• Explanation: This law is essentially energy conservation applied to thermodynamic systems.

13. Flywheel

• Definition: A device that stores rotational energy and helps smooth fluctuations in rotational speed.
• Application: Used in engines to maintain a constant speed, even during irregular power delivery.

14. Four-Stroke Engine

• Definition: An engine cycle with four stages: induction, compression, expansion, and exhaust.
• Explanation: Fuel burns once every four strokes, making the process efficient for internal combustion engines.

15. Indicated Power

• Definition: The total power developed within an engine's cylinders.
• Explanation: Indicated power is an ideal measure and often exceeds brake power due to frictional losses within the engine.

16. Indicator Diagrams

• Definition: Pressure-volume (p-V) diagrams that illustrate the performance of an engine cycle.
• Application: These diagrams help engineers assess an engine's efficiency and work output per cycle.

17. Isothermal Process

• Definition: A thermodynamic process where temperature remains constant.
• Explanation: In isothermal processes, any added or removed heat directly changes the work done, without altering internal energy.

18. Isotherms

• Definition: Lines on a p-V diagram representing constant temperature.
• Application: Isotherms allow visualisation of temperature differences within thermodynamic cycles.

19. Mechanical Efficiency

• Definition: The ratio of brake power to indicated power.
• Explanation: This efficiency measure highlights power lost to friction and other inefficiencies in mechanical systems.

20. Moment of Inertia

• Definition: The rotational equivalent of mass, defined as the product of mass and the square of the radius from the rotation axis.
• Formula: $I = mr^2$ (for a point mass), or for extended objects, moments of inertia are summed.
• Explanation: Higher moments of inertia make objects harder to spin or stop, analogous to inertia in linear motion.

21. Overall Efficiency

• Definition: The ratio of output power to total input power, taking into account all sources of power loss.
• Application: Overall efficiency is crucial for evaluating complete systems, especially in engines and machines.

22. Reversed Heat Engine

• Definition: A heat engine working in reverse, transferring heat from a cold to a hot reservoir.

23. Rotational Kinetic Energy

• Definition: Energy due to the rotation of an object, calculated as half the product of the moment of inertia and the square of angular velocity.
• Formula: $E = \frac{1}{2} I \omega^2$
• Explanation: This energy is analogous to linear kinetic energy but applies to rotating systems.

24. Second Law of Thermodynamics

• Definition: A law stating that energy transfers and transformations are irreversible and that no heat engine can be 100% efficient.
• Explanation: This law establishes limits on engine efficiency and introduces the concept of entropy.

25. Sink

• Definition: The part of an engine where waste heat is released, usually at a lower temperature than the source.
• Explanation: A cooler sink allows better efficiency, as it increases the temperature difference from the source.

26. Source

• Definition: The energy input for an engine, typically at a higher temperature than the sink.
• Explanation: Greater temperature differences between source and sink improve engine efficiency.

27. Theoretical Diesel Engine

• Definition: An idealised engine cycle involving adiabatic compression and expansion with heat added at constant pressure.
• Explanation: Diesel engines rely on compression ignition rather than spark ignition, creating different efficiency characteristics from petrol engines.

28. Theoretical Otto Cycle

• Definition: An ideal cycle involving adiabatic compression and expansion with heat added at constant volume.
• Explanation: This cycle models spark-ignition engines, such as petrol engines, focusing on maximising work done.

29. Thermal Efficiency

• Definition: The ratio of indicated power to input power.
• Explanation: Higher thermal efficiency indicates better conversion of heat into work within an engine.

30. Torque

• Definition: A force that produces rotational motion, equal to the product of force and perpendicular distance to the axis of rotation.
• Formula: $\tau = F \times r$
• Explanation: Torque is essential in engines, where it measures the twisting force on a rotating shaft, influencing acceleration and power.