Thermodynamics is a branch of Physics that can be applied to any system in which thermal processes are important, although we will concentrate on systems in thermal equilibrium. It is based on four laws (derived from experimental observation) and makes no assumptions about the microscopic character of the system. It is therefore very powerful and very general. We will introduce these laws, consider their consequences and apply them to some simple systems.
The module will prepare you for applications in different branches of Physics and provide a foundation for the model-dependent statistical mechanics approach.
Module learning outcomes
On completion of this course the student will be able to -
Define and explain fundamental concepts such as system, state function, quasistatic reversible process, thermodynamic equilibrium and equation of state.
State the Zeroth Law of Thermodynamics; explain how this leads to the definition of empirical temperature, describe how the International Temperature Scale is realised and perform calculations related to empirical temperature scales.
State the First Law of Thermodynamics and show how this leads to a definition of the internal energy, U, as a state function and to the conservation law dU = dW + dQ.
Define bulk parameters, such as the principal heat capacities, and perform calculations requiring application of the First Law.
Explain the concept of an ideal reversible heat engine, describe a Carnot cycle and derive the efficiency of a Carnot engine.
State the Kelvin-Planck and Clausius forms of the Second Law of Thermodynamics and show they are equivalent. Use this law to prove Carnotâ theorem and its corollary.
Show how thermodynamic temperature may be defined from the Second Law. Perform calculations relating to ideal engines, refrigerators and heat pumps.
Derive Clausiusâ theorem from the Second Law and show how this theorem leads to the definition of entropy, S. Prove that S is a state function. Derive the entropy form of the First Law. Calculate entropy changes for simple irreversible processes.
Define the Helmholtz and Gibbs functions and show how these are related to conditions of thermodynamic equilibrium.
Derive the four Maxwell relations for systems with two degrees of freedom and use them in calculations and derivations.
Define the order of a phase transition in terms of derivatives of the Gibbs function.
Derive the Clausius-Clapeyron equation for a first order phase transition and apply it to solid-liquid, liquid-vapour and solid-vapour phase transitions. Obtain Ehrenfestâ equations for second order transition.
State the Third Law of Thermodynamics and describe some of the consequences for the behaviour of systems at low temperatures.
Discuss and use (in quantitative calculations) the fundamental ideas of thermodynamics in a range of systems such as (i) showing that U is independent of T for an ideal gas; (ii) deriving the TdS equations and use them to describe the behaviour of the principal specific heat capacities; (iii) applying a thermodynamic approach to the elastic deformation of a rod; (iv) deriving the equations for the Joule and Joule-Kelvin coefficients and explaining how the Joule-Kelvin effect is used in the liquefaction of gases; (v) the thermodynamic analysis of black body radiation etc.