# PX145 Physics Foundations

##### Weighting: 12 CATS

This module looks at dimensional analysis, matter and waves. Often the qualitative features of systems can be understood (at least partially) by thinking about which quantities in a problem are allowed to depend on each other on dimensional grounds. Loosely speaking this is the requirement that "apples can only equal apples". Examples looked at include the size of an atom, the length scale on which a theory of gravity has to take account of quantum effects and the speed of a wave in a shallow channel. The module then covers thermodynamics which is the study of heat transfers and how they can lead to useful work. How much useful work can be extracted from a heat engine is determined by a quantity called the entropy. Even though the results are universal, the simplest way to introduce this topic is via the ideal gas, whose properties are discussed and derived in some detail.

The second half of the module covers waves. Waves are time-dependent variations about some time-independent (often equilibrium) state. For example, they can be variations in pressure (sound waves), variations in electric and magnetic fields (light waves) or variations in the height of water above the sea-bed (water waves). They carry energy, momentum and information and much of their behaviour is similar whatever their nature. The module revises the relation between the wavelength, frequency and velocity and the definition of the amplitude and phase of a wave. It also covers phenomena like the Doppler effect (this is the effect that the frequency of a wave changes as a function of the relative velocity of the source and observer), the reflection and transmission of waves at boundaries and some elementary ideas about diffraction and interference patterns.

Aims:
To introduce the style and content of physics at university and to cover key ideas about waves, matter and thermodynamics.

Objectives:
At the end of the module you should:

• Be able to use dimensional analysis to establish how physical quantities can depend on each other
• Know about the solid, liquid and gas phases of matter and how their properties depend on thermal motion and the forces between atoms and molecules
• Have a working knowledge of the kinetic theory of gases and how this relates to what is observed in real gases
• Be able to explain and use the first and second laws of thermodynamics to solve problems involving heat transfers and work
• Be able to recognise the wave equation and understand its origin.
• Be able to solve wave problems involving travelling waves, the Doppler effect, boundary conditions and normal modes in a string or pipe.
• Understand the nature of light: its electromagnetic origin, its polarization and the role of the refractive index
• Be able to describe interference effects and have acquired a familiarity with the use of complex number notation.

Syllabus:

Introduction to University Physics
Concepts - Mechanics, Fields and Thermal physics. Their use to predict and explain phenomena. The need for mathematics.

Dimensional Analysis
Relation between dimensions and units. A physical law can always be written using dimensionless variables. Illustrative examples: wavespeed in a shallow channel and along a tight string; GI Taylor's t2/5 law for the spread of a fireball, the Planck length, period of a pendulum and the role of a second dimenionless variable.

Heat and Gases
Thermal equilibrium, zero'th law. Temperature scales. Thermal expansion. Heat capacity. Phases of Matter. Kinetic theory of gases: equation of state and isotherms, kinetic model of gases, equipartition of energy. Heat capacity, compressibility. Particle interactions, van der Waal's equation, condensed phases. First law of thermodynamics. Thermodynamic systems and processes. Conservation of energy, heat is a form of energy. Internal energy and heat capacity. Adiabatic processes. Second law of thermodynamics. Reversible and irreversible processes. Carnot cycles, heat engines, refrigerators and heat pumps.

Waves
Types of wave: sound waves in gases and solids, water waves, light waves. Different elastic moduli in solids. Description of a travelling wave and relation between speed, frequency and wavelength/wavenumber. Idea of a plane wave and use of complex numbers. Impedance, power and intensity. Reflection and transmission at a boundary, standing waves, normal modes and beats. Doppler effect. Nature of Light: wavefronts, reflection and refraction, refractive index, polarization. Huygens construction. Coherence. Interference: interference in thin films, interference of light waves from coherent sources. Two-slit experiment, intensity in interference pattern. Phase difference and path difference.

Commitment: 29 Lectures + 10 problems classes

Assessment: 2 hour examination

Recommended Texts: H D Young and R A Freedman, University Physics, Pearson.