85 lines
4.4 KiB
Markdown
85 lines
4.4 KiB
Markdown
---
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title: Thermodynamics
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created_date: 2024-12-05
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updated_date: 2024-12-05
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aliases:
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tags:
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---
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# Thermodynamics
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## Course Recap
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- Different primary energy forms (chemical, nuclear, solar, kinetic) need to be converted into useful energy (mechanical, electrical).
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- Applications are engines, aircraft/rocket propulsions, wind turbines, fuel cells, steam and gas turbines, combustion, compressors, pumps
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- Thermodynamics provides us with tools for design, performance assessment, improvements and optimization.
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- Efficiencies: generally speaking is the desired output divided by the required input.
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- $$ \eta_{thermal} = \frac{Useful work/energy}{energy provided}$$
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- Total efficiency is usually the multiplication of each individual stage
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- $\eta_{total}=\eta_{compressor} \eta_{turbine} \eta_{generator}$
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- Examples
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- Combustion: gasoline ~35%, diesel ~42%
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- fossil power production: ~35-48%
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- solar thermal power production: ~18-22%
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### Laws of Thermodynamics
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> [!important] 0th law: Equilibrium
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> If two systems are both in thermal equilibrium with a third system, then they are in equilibrium with each other.
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This law establishes the concept of temperature, which is a fundamental and measurable property. This allows to measure and compare systems and states.
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We have different kinds of equilibriums: mechanical (pressure), thermal (temperature), phase (mass of each phase doesn't change) and chemical (chemical composition does not change with time).
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> [!important] 1st law: Energy Conversation
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> The change in internal energy of a closed system is equal to the heat added to the system minus the work done by the system on its surroundings
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> $$ \Delta U = Q - W$$
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Energy is conserved: it cannot be created nor destroyed. The two forms of energy are heat and work.
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> [!important] 2nd law: Entropy
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> In any natural thermodynamic process, the total entropy of a system and its surroundings always increases.
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Every system evolves towards thermodynamic equilibrium, which has the greatest entropy amongst the states accessible to the system.
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Entropy measures disorder and randomness. It implies that some energy is always dispersed as heat, increasing the overall entropy
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> [!important] 3rd law: Absolute Zero
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> As the temperature of a system approaches absolute zero, the entropy of a perfect crystal approaches a constant minimum.
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This implies that we typically assume 0 entropy at 0° Kelvin.
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### Thermodynamic System, State and Properties
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A system consists of a boundary which separates the system from the surroundings. Energy transfer across the boundary can happen through work, heat or mass transfer.
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- *Adiabatic*: a system without heat transfer
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- *non-adiabatic*: a system with heat transfer
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- *closed*: a system without mass transfer
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- *open*: a system with mass transfer
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- *isolated*: a system without any energy transfer
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The thermodynamic state is defined as the set of thermodynamic properties the characterise the state, independently of the form of the system and the process through which it was achieved.
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#### Properties
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Properties can be *intensive* (also called *specific*, non-mass dependent, lower-case letter) or *extensive* (mass dependent, Upper-case letter). The molar state is a lower case with tilde ($\tilde u$)
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- V, volume, [m3]
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- p, pressure, [Pa]
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- U, internal energy, [J]
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- T, temperature, [K]
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- H, enthalpy, [J]
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- S, entropy, [J/K]
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- F, Helmholtz free energy, [J]
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- G, Gibbs free energy, [J]
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#### Processes
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Processes are a change from one state to another. This is best visualized on a pV-graph as the line connecting two state points.
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- Isothermal (T=const)
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- Isobaric (b=const)
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- Isochoric (v=const)
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- Isentropic (s=const)
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- Adiabatic ($\dot Q=0$)
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#### Cylces
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A *cycle* is a series of processes that return the system to initial state. (On a pV-graph this returns to the original state and thus forms a loop.)
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There are two classes of cycles: power cycles and refrigeration/heat pump cycles.
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- *Power cycles* use temperature differences to create work and refrigeration cycles use work to create heat transfer ($Q_{in} > Q{out}$).
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- Efficiency: $\eta_{th}=\frac{W_{cycle}}{Q_{in}} = 1-\frac{Q_{out}}{Q_{in}}$
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- *Refrigeration cycles*: With aid of work move heat from cold reservoir to a hot reservoir (against natural process) ($Q_{out} > Q_{in}$).
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- Efficiency: $COP_{cooling}=\frac{Q_{in}}{W_{cycle}} = \frac{Q_{in}}{Q_{out}-Q_{in}}$
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- Efficiency: $COP_{heating}=\frac{Q_{out}}{W_{cycle}} = \frac{Q_{out}}{Q_{out}-Q_{in}} = COP_{cooling} + 1$
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