add uncommitted year 1 content

uni/mmme/1xxx/1048_thermodynamics_and_fluid_mechanics/thermodynamics.md

@@ -547,3 +547,90 @@ $$Q = m (c_v-c_v)(T_2-T_1) = 0 $$
 
 This proves that the isentropic version of the process adiabatic (no heat is transferred across the
 boundary).
+
+# 2nd Law of Thermodynamics
+
+The 2nd Law recognises that processes happen in a certain direction.
+It was discovered through the study of heat engines (ones that produce mechanical work from heat).
+
+> Heat does not spontaneously flow from a cooler to a hotter body.
+
+~ Clausius' Statement on the 2nd Law of Thermodynamics
+
+> It is impossible to construct a heat engine that will operate in a cycle and take heat from a
+> reservoir and produce an equivalent amount of work.
+
+~ Kelvin-Planck Statement of 2nd Law of Thermodynamics
+
+
+## Heat Engines
+
+A heat engine must have:
+
+- Thermal energy reservoir --- a large body of heat that does not change in temperature
+- Heat source --- a reservoir that supplies heat to the engine
+- Heat sink --- a reservoir that absorbs heat rejected from a heat engine (this is usually
+  surrounding environment)
+
+![](./images/vimscrot-2022-03-22T09:17:36,214723827+00:00.png)
+
+#### Steam Power Plant
+
+![](./images/vimscrot-2022-03-22T09:19:07,697440371+00:00.png)
+
+## Thermal Efficiency
+
+For heat engines, $Q_{out} > 0$ so $W_{out} < Q_{in}$ as $W_{out} = Q_{in} - Q_{out}$
+
+$$\eta = \frac{W_{out}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}$$
+
+Early steam engines had efficiency around 10% but large diesel engines nowadays have efficiencies
+up to around 50%, with petrol engines around 30%.
+The most efficient heat engines we have are large gas-steam power plants, at around 60%.
+
+## Carnot Efficiency
+
+The maximum efficiency for a heat engine that operates reversibly between the heat source and heat
+sink is known as the *Carnot Efficiency*:
+
+$$\eta_{carnot} = 1 - \frac{T_2}{T_1}$$
+
+where $T$ is in Kelvin (or any unit of absolute temperature, I suppose)
+
+Therefore to maximise potential efficiency, you want to maximise input heat temperature, and
+minimise output heat temperature.
+
+The efficiency of any heat engine will be less than $\eta_{carnot}$ if it operates between more than
+two reservoirs.
+
+## Reversible and Irreversible Processes
+
+### Reversible Processes
+
+A reversible process operate at thermal and physical equilibrium.
+There is no degradation in the quality of energy.
+
+There must be no mechanical friction, fluid friction, or electrical resistance.
+
+Heat transfers must be across a very small temperature difference.
+
+All expansions must be controlled.
+
+### Irreversible Processes
+
+In irreversible processes, the quality of the energy degrades.
+For example, mechanical energy degrades into heat by friction and heat energy degrades into lower
+quality heat (a lower temperature), including by mixing of fluids.
+
+Thermal resistance at both hot sources and cold sinks are an irreversibility and reduce efficiency.
+
+There may also be uncontrolled expansions or sudden changes in pressure.
+
+# Energy Quality
+
+## Quantifying Disorder (Entropy)
+
+$$S = k\log_eW$$
+
+where $S$ is entropy, $k = 1.38\times10^{-23}$ J/K is Boltzmann's constant, and $W$ is the number of
+ways of reorganising energy.s