The Absolute Minimum of Thermodynamics

This is the absolute minimum that you must know to have a viable understanding of ordinary, non-statistical thermodynamics. This checklist follows the development given in D. Elwell and A. J. Pointon, Classical Thermodynamics. Penguin, 1972. Read it in parallel with this checklist. It follows the standard development of thermodynamics. You should be able to answer the questions given in italics.

Properties describing thermodynamic systems are macroscopically measurable:
mass, volume, density, specific heat, dielectric constant, elastic moduli, magnetic
permeability, surface tension, thermal expansion coefficient, thermal conductivity
etc.
What is a property of a thermal system that lies outside ordinary thermodyanmics? Hint: think molecular.

Zeroth law of thermodynamics
How does it lead to the notion of temperature?

First law of thermodynamics. dQ = dU + dW
What are Q, U and W? How is heat defined in the context of this law?

Intensive versus extensible properties
How the general expression for work is given as
dW = (intensive magnitute) d(extensive magnitude)

A thermodynamic state space
State functions
Draw the trajectory of an isothermal expansion of an ideal gas in PV state space.
What area on the diagram represents work?

Inexact versus exact differentials.
How does the difference matter for the defining of state functions?

Reversible vs irreversible processes
(Important! If you don't get this, then the second law will never make sense.)
Give an example of a reversible and an irreversible process? Why are they so?

Various different statements of the second law in terms of impossible devices:

(Clausius) It is impossible to construe/ a self-acting device that, operating in a cycle, will
produce no other effect than the transfer of heat from a cooler to a holler body.
(Thomson) It is impossible to construct an engine that, operating in a cycle, will produce no
other effect than the extraction of heat from a reservoir and the performance of an
equivalent amount of work.

and the more familiar

In any thermodynamic process the entropy of the universe will increase or remain
constant but will never diminish.

Carnot's principle
No engine operating between two given reservoirs can be more efficient than a
Carnot engine operating between the same two reservoirs.

How is Carnot's principle proved by means of coupled heat engines?

The thermodynamic scale of temperature

How is the scale defined by the coupling of heat engines?

Clausius inequality

Integral for a circular process dQ/T > 0 for irreversible process
Integral for a circular process dQ/T = 0 for reversible process

Definition of entropy as dS = dQ/T

How does the Clausius inequality enable us to conclude that entropy is a state function?
How does the Clausius inequality lead to the form of the second law that ΔS>0 for real processes.

The Third Law of Thermodynamics

Does the third law apply to a classical (i.e. non-quantum) ideal gas?
Hint: No.
How can that be?