thermodynamics

Thermodynamics is important and very present in our lives•1.1 Using Thermodynamics

System: the object/objects that are being studied•Surroundings: Everything external to the system•

Note: this boundary does not have to be a physical boundary○

Boundary: The split between the system and surroundings•

Note: the term control mass can be used interchangeably with closed system

Closed System: a system with a fixed quantity of matter○

Note: the term control volume can be used interchangeably with open system

Open System: A region of space through which mass may flow○

Control surface: A fancy way of saying "system boundary" (This is what I gleaned from the book. Is this correct?)

○

Types of systems•

1.2 Defining Systems

Closed System: As stated above, a closed system is a system of constant matter/mass•Isolated System: A type of closed system that does not interact in any way with its surroundings. This means no energy/mass transfer.

•

1.2.1 Closed Systems

Control Volume: A system of which mass may cross its boundaries•1.2.2 Control Volumes

What is happening at the system boundaries○

Why is the system being studied○

Keep two things in mind when selecting system boundaries•1.2.3 Selecting the System Boundary

1.3 Describing Systems and Their Behavior

Also known as classical thermodynamics○

Macroscopic perspective: concerned with the overall behavior of a system•

Also known as statistical thermodynamics○

This perspective is used to study internal energy and entropy○

Microscopic perspective: concerned with the structure of the matter of the system•

1.3.1 Macroscopic and Microscopic Views of Thermodynamics

ex: mass, volume, energy, pressure, and temperature○

Property: a macroscopic characteristic of a system to which a numerical value can be assigned without knowledge of previous behavior of the system.

•

State: condition of a system as describe by it properties•Process: when a system's state changes as a result of a change in the properties of a system. So a process is a transformation from one state to another.

•

Steady State: A type of state in which none of a system's properties change with time.•

1.3.2 Property, State, and Process

ex: mass, volume, and energy○

Extensive Property: A properties is extensive if it is an overall value for a system that is dependent on the size of a system

•

ex: pressure and temperature○

Intensive Properties: A properties that is independent of the size/extent of a system•

1.3.3 Extensive and Intensive Properties

There are multiple types of equilibrium: mechanical, thermal, phase, and chemicalEquilibrium: A balance of forces and other influences•

1.3.4 Equilibrium

Chapter 1Saturday, June 23, 2012 2:53 PM

New Section 1

There are multiple types of equilibrium: mechanical, thermal, phase, and chemical○

Equilibrium State: If a system in question does not change with time.•

Base Units: a primary set of dimensions•

Quantity SI English

Mass kg (Kilogram) lb (Pound)

Length m (Meter) ft (Foot)

Time sec (Second) sec (Second)

Force N (Newton) lbf (pound force)

•

1.4 Measuring Mass, Length, Time and Force

Specific Volume: Reciprocal of density (Volume per unit mass)•

Notation for molar basis: a bar over the variable○

Molar basis: A fancy way of saying "express a number in terms of moles"•

1.5 Specific Volume

Absolute Pressure: Pressure with respect to the zero pressure of a vacuum•Buoyant Force: The resulting pressure force acting on a body as a result from submerging a body--completely or partially-- in a liquid

•

Absolute Pressure: Pressure as related to the zero pressure of a vacuum•Gage/Vacuum Pressure: Pressure as related to the pressure of the surroundings•

1.6 Pressure

Zeroth Law of Thermodynamics: Two objects are in thermal equilibrium with a third object if they are in thermal equilibrium with onanother.

•

Thermometric Property: any object that has at least one measureable property that changes as its temperature changes. The object that has this property is called a thermometric substance

•

○

Kelvin (SI) vs Rankine(English) Scale•

○

Celsius vs Kelvin•

○

Fahrenheit vs Rankine•

○

Fahrenheit vs Celcius•

1.7 Temperature

1)

2)

3)

: densitya. : acceleration constantb. : Difference in heightc. : Choose this accordingly depending on the relation of the two pressure exerting substances

d.

4)

5)

Equations

New Section 1

2.1 Reviewing Mechanical Concepts of Energy

Kinetic Energy is a property. We can determine KE just by looking determining the mass and velocity of the object. How the object obtained the mass and velocity is insignificant to determining KE.

○

Furthermore, KE is an extensive property as it depends on mass, and is thus dependent on the size of the system.

○

Kinetic Energy:

•

: Force○

: displacement○

Work:

•

2.1.1 Work and Kinetic Energy

: mass of object○

: gravitational constant○

: height of object○

Potential Energy: •

Potential energy is also an extensive property. The rational is very much like the explanation for KE.

•

2.1.2 Potential Energy

Energy has the SI unit , or also known as the Joule •The English system unit is foot-pound force: •

2.1.3 Units for Energy

Ideally, energy is conserved such that •2.1.4 Conservation of Energy in Mechanics

Thermodynamic Definition of Work: Work is done by a system on its surroundings if the sole effect on everything external to the system could have been the raising of a weight. (Still don't understand this…)

•2.2 Broadening Our Understanding of Work

If , work is done by the system on its surroundings○

If , work is done on the system by its surroundings○

Work•

Note: work is not a property. Rather, it is a process of energy transfer. System states do not have a "work property"

•

Contrast this with the difference in properties of two states. We can find the exact value of

the difference, and thus (for the case of mass)

○

The differential of work is inexact because it cannot be evaluated without knowing specific details

of the process between two states. Thus work is preceded with a delta :

(Why again is

this inexact?: this embodies the idea that there are a lot of different ways to get from one state to the other)

•

2.2.1 Sign Convention and Notation

Power is the product of force and velocity.

The dot appearing above the indicates that the variable is a time rate

Also note that total work can be calculated from the above equation:

○

Power: The rate of energy transfer•

The SI unit for power is

, also known as the watt

2.2.2 Power

Chapter 2Monday, June 25, 2012 1:41 PM

New Section 1

The SI unit for power is

, also known as the watt•

Ultimately, we can conclude that

(Here, are we allowed to remove the delta

because we are now integrating over a property?)

○

Work From Compressing a Piston: •2.2.3 Modeling Expansion or Compression of Work

This idealization is like the idea of a point mass, it makes our lives easier as we study thermodynamics. This allows us to make predictions such as changing the volume of a closed system of gas will predictably change pressure as determined by the equation

○

Quasiequilibrium/quasistatic Process: All states are equilibrium states (Is this correct?)•

Polytropic Process: A quasiequilibrium process described by an equation similar to , where is a constant

•

2.2.5 Expansion or Compression Work in Quasiequilibrium Processes

: normal stress acting at the end of the bar○

: cross sectional area of bar○

: Initial length of bar○

: Final length of bar○

Extension of a Solid Bar:

•

: Surface tension (Is this calculated or a given?)○

: change in area○

Streching of a Liquid Film:

•

: Torque on shaft○

: angular velocity○

Power Transmitted by a Shaft: •

: potential difference○

: current○

: amount of electrical charge that flows into the system

On a similar note, work can be expressed as ○

Electric Power: •

2.2.6 Further Examples of Work

Internal Energy : All kinds of energy aside from kinetic and potential energy•Total change in energy: •

Contributors to internal energy: translational kinetic energy, rotational kinetic energy, vibrational kinetic energy

○

Microscopic interpretation of internal energy: this is the energy stored in the configuration and motion of molecules.

•

2.3 Broadening Our Understanding of Energy

2.4 Energy Transfer by Heat

If , heat is transferred into the system○

If , heat is transferred out of the system○

Sign notation•

Note: this sign notation is the opposite of the system used for work•Heat, like work is not a property. It is a means of energy transfer•

Total amount of energy transferred through heat:

○

Rate of Heat Transfer : the rate of energy transfer through heat•

Is this a surface integral?○

Heat Flux : rate of heat transfer per unit area. Related to rate of heat transfer via following

equation:

•

Adiabatic Process: A process without heat transfer.•

2.4.1 Sign Convention, Notation, and Heat Transfer Rate

2.4.2 Heat Transfer Modes

New Section 1

: proportionality constant

: Area

: Temperature gradient (If linear gradient, can be as simple as

)

Rate of heat transfer:

○

Conduction: Transfer of energy from more energetic particles of a substance to adjacent particles that are less energetic

•

: emissivity (A measure of how efficiently the surface radiates

: Stefan-Boltzman Constant

: Surface Area

: absolute temperature of the surface

Rate of heat transfer: ○

Radiation: Energy transmitted by electromagnetic waves. This mode of heat transfer does not require a medium-- unlike conduction

•

: Temperature of solid surface

: Temperature of adjacent gas/liquid

: heat transfer coefficient

: surface area of solid surface

Rate of heat transfer from surface to gas/liquid (Newton's law of cooling):

○

Convection: Energy transfer between a solid surface at temperature and an adjacent gas or liquid

•

2.4.2 Heat Transfer Modes

First Law of Thermodynamics: Energy is conserved•

In other words, ○

Change in amount of energy contained within a system during a time interval = net amount of energy transferred in across system boundary by heat during the time interval - net amount of energy transferred out across the system boundary by work during the time interval

•

2.5 Energy Accounting: Energy Balance for Closed Systems

Time rate form of Energy Balance:

•

2.5.1 Important Aspects of the Energy Balance

Thermodynamic Cycle: sequence of processes that begin and end at the same state. So at the end of a cycle, all properties return to their original values

•2.6 Energy Analysis of Cycles

•

Consider an energy cycle that works with a hot and cold body•

2.6.1 Cycle Energy Balance

This means that less heat is output than the total heat put in because some of the input heat is changed into work

○

Heat from hot body into cycle then out of cycle into cold body○

Power Cycle: A thermodynamic cycle that does net work onto its surroundings with each cycle•

Thermal Efficiency:

or

•

2.6.2 Power Cycles

○

Heat from cold body into cycle the out into hot body○

Work is done on the system so that more heat is output than the amount of heat input into the system.

•

Coefficient of performance :

or

○

Refrigeration cycle: the purpose is to cool a body and pump heat into surroundings (hot body)•

Heat Pump Cycles: The purpose is to heat a body by using work and drawing from a colder body•

2.6.3 Refrigeration and Heat Pump Cycles

New Section 1

Coefficient of Performance :

or

○

Heat Pump Cycles: The purpose is to heat a body by using work and drawing from a colder body•

It is desirable to have large coefficients of performance•2.7 Energy Storage

Batteries: very popular method of energy storage, yet they are heavy, take long to recharge, have short lifetimes, and can't hold very much charge-- relatively speaking

•

Ultra Capacitors: Have a longer lifetime than batteries and can be charged and discharged very rapidly.

•

Superconducting Magnetic Systems: Store energy in a magnetic field in a cold superconducting material. Instantaneous and efficient energy delivery.

•

Fly Wheels: Store energy as kinetic energy. Also a very efficient way of storing energy•Hydrogen: not a very efficient way of storing energy. Energy is stored by breaking apart water and storing the hydrogen. Then by allowing the hydrogen to combine with oxygen to form water, energy is released.

•

2.7.2 Storage Technologies

: Drag force○

: drag coefficient○

: Frontal Area○

: air density○

: velocity○

Aerodynamic drag:

•

Miscellaneous Equations

represent position such that displacementa.

1)

F: Forcea.V: Velocityb.

Power: 2)

a.

Work from changing volume3)

Equations

New Section 1

Phase: A quantity of matter that is homogeneous throughout both chemical composition and physical structure

•

Pure Substance: A substance that is uniform and invariable in chemical composition•

Simple Compressible Systems: This is a type of system that requires two independent thermodynamics to have fixed a state.

○

State Principle: A guide that determines the number of independent states required to fix a state•

3.1 Getting Started

P-V-T Surface: This surface relates the three elements pressure volume and temperature to one another

•

Two-Phase Regions: located between single-phase regions. These are areas where two phases can exist in equilibrium

•

Triple line: A line on the p-v-t surface on which all three phase can exist simultaneously•Saturation State: state at which a phase change begins or ends•Vapor Dome: a dome shaped region enclosing liquid-vapor states (Is this correct?)•Critical Point: The point where vapor and liquid become indistinguishable•

3.2 p-v-T Relation

Projections of the p-v-t Surface

Phase Diagram: the p-v-t surface projected onto the p-v plane•Saturation Temperature: The temperature at which a phase change takes place for a given pressure.

•

Saturation Pressure: The pressure at which a phase change takes place for a given temperature.•Triple Point: The triple line projected onto the pv plane, which results in a point.•Pressure-Volume:(For these figures, are the lines temperature gradients?)•Temperature-Volume: Relate temperature to volume•

Pressure-Temperature

3.3 Studying Phase Change

Subcooled liquid (Also Compressed Liquid): a state in which a substance is at a temperature cooler •

Chapter 3Thursday, June 28, 2012 7:40 PM

New Section 1

On the above graph, this is line . This is a state of pure water○

Subcooled liquid (Also Compressed Liquid): a state in which a substance is at a temperature cooler than the saturation temperature of a given pressure.

•

○

.

Extension: We can also find the ratio of mass of liquid to total mass of mixture○

This is line . This is the portion that represents phase change (Correct?)○

Also note that for a higher the pressure, a higher temp is required to enter the vapor dome. This is so because it takes more energy to boil at a higher pressure.

○

Quality: ratio of mass of vapor to total mass of the mixture (mixture is composed of vapor and fluid)

•

This is line . This represents the vapor phase of a liquid. (Correct?)○

Superheated vapor: a state in which a substance is at a temperature greater than the saturation temperature of a given pressure

•

Two-phase liquid-vapor mixture

Steam Tables: table that gives properties of water in the vapor phase•3.4 Retrieving Thermodynamic Properties

When looking at a p-t graph, how can we relate pressure and density? I am having trouble grasping the relationship

•

Using slope, approximate the value of the unknown value○

Linear Interpolation: Method used to approximate values not present in given tables•

3.5 Evaluating Pressure, Specific Volume, and Temperature

○

Average specific volume•3.5.2 Saturation Tables

: Internal Energy○

: Pressure○

: Volume○

Enthalpy(H): •

○

○

Finding the specific enthalpy/internal energy of a two phase liquid-vapor mixture•

3.6 Evaluating Specific Internal energy and Enthalpy

Reference States/Reference Values: The state/value that the numbers on a table are compared to.•3.6.3 Reference States and Reference Values

Constant Volume:

○

Constant Pressure:

○

Specific Heat Ratio:

○

Specific Heats: Intensive properties defined as follows•3.9 Introducing Specific Heats

○

○

Specific volume and specific internal energy change very little with changing pressure at a fixed temperature. Thus, we can approximate that

•

○

This can finally be approximated to ○

Thus, enthalpy can be expressed as follows•

3.10 Evaluating Properties of Liquids and Solids

New Section 1

So just like specific volume and specific internal energy, specific enthalpy can be approximated to only depend on temperature

○

This ultimately simplifies calculations involving liquids and solids as internal energy only depends on temperature.

○

So for incompressible substances, specific heat does not depend on pressure. Just temperature. Furthermore,

○

However, enthalpy depends on both temperature and pressure○

So for incompressible substances,○

Incompressible Substance Model: Can be applied to all solids and liquids. This model is the idea that the specific volumes of these phases varies little and the specific internal energy mainly varies with temperature

•3.10.2 Incompressible Substance Model

Or,

where

○

Compressibility Factor:

•

What is the significance of the generalized compressibility chart?•

3.11 Generalized compressibility Chart

□

IF specific heat is constant,

○

Change in specific internal energy•

□

IF specific heat is constant,

○

Change in specific enthalpy•

○

or ○

Also recall that

○

Relationship between specific heats (Is this always true?)•

3.13 Internal Energy, Enthalpy, and Specific Heats of Ideal Gases

New Section 1

4.1 Conservation of Mass for a Control Volume

: Rate of mass change in control volume○

: Rate of mass entering ○

: Rate of mass exiting○

are mass flow rates○

Conservation of Mass:

•

○

Mass Rate Balance: this is just a more general version of the conservation of mass principle that accounts for multiple inlets and outlets

•

: density

: Velocity component normal to surface of inlet/exit (This is )

A: Area of inlet

: Product known as mass flux

So this should be a double integral

○

Mass Rate Flow Integral•

4.1.1 Developing the Mass Rate Balance

4.2 Forms of the Mass Rate Balance

Flow is normal to the boundary at locations were mass enters or exits the control volume○

All intensive properties are uniform with position over each inlet/exit area○

Flow can be considered to be One-Dimensional Flow if it meets the following requirements:•

: mass flow rate

: density

: Area

: Velocity

: specific volume

: This product is the volumetric flow rate

○

When flow is one-dimensional, we can use the following equations to find mass flow rate•

○

Updated Mass Rate Balance Equation•

4.2.1 One-Dimensional Flow Form of the Mass Rate Balance

•

4.2.2 Steady-State Form of the Mass Rate Balance

Look here for practice problems•4.3 Applications of the Mass Rate Balance

○

Energy Rate Balance:•4.4 Conservation of Energy for a Control Volume

4.5 Analyzing Control Volumes at Steady State4.5.1 Steady-State Forms of the Mass and Energy Rate Balances

Chapter 4Sunday, July 08, 2012 4:48 PM

New Section 1

○

Also, rate of mass entering control volume is equal to rate of mass exiting the control volume, thus

○

Ultimately, we can simplify our steady state equation to○

Steady State Equation•

For our ease, we will make assumptions which will allow us to use the steady state equation

•

4.5.1 Steady-State Forms of the Mass and Energy Rate Balances

Nozzle: a flow passage of varying cross sectional area in which the velocity of a gas or liquid increases in the direction of flow

•

Diffuser: a flow passage of varying cross sectional area in which the velocity of a gas or liquid decreases in the direction of flow

•

No heat lost

No work done

No change in potential energy

○

Result:○

Enthalpy is exchanged with kinetic energy

Interpretation:○

Steady State Analysis•

4.6 Nozzles and Diffusers

Turbine: A device in which power is developed as a result of gas or liquid passing through a set of blades attached to a shaft free to rotate.

•

No heat lost

Work is done

No change in velocity

No change in potential

○

○


4.7 Turbines

Compressors/Pumps: Devices in which work is done on the substance flowing through them in order to change the state of the substance (such as pressure or elevation)

•

Assume no heat loss

Assume no change in velocity

Assume no change in potential

○

○


Note: Same equation as turbines, except for compressors/pumps, work is negative, while for turbines, work is positive.

•

4.8 Compressors and Pumps

Heat Exchanger: A device that exchanges heat•Steady State analysis•

4.9 Heat Exchangers

New Section 1

No work done



No change in heat as all heat exchange occurs within the control volume

○

(Do we need mass flow rate here?)○

Steady State analysis•

Note: heat exchanges just facilitate change in enthalpy•

Throttling Device: A device that controls rate of flow•

No heat exchange

No work done



○

○


Note: throttling devices just control the rate of flow.•

4.10 Throttling Devices

These types of components can often be combined to form systems, which then need to be analyzed.

•4.11 System Integration

Transient: a period of time during which the state of a device changes.•4.12 Transient Analysis

are the total amounts of mass that have, respectively, entered and exited the control volume between time and . The integral form is below

○

•

4.12.1 The Mass Balance in Transient Analysis

Change in internal energy is equal to any heat/work transfer and amount of entropy that entered/exited the system

○

Like the case for mass balance○

•

4.12.2 The Energy Balance in Transient Analysis

New Section 1

We can use spontaneous processes to develop work•Clausius Statement of the Second Law: It is impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from a cooler to a hotter body

•

Analytical Version: ○

I'm don't quite understand the Kelvin-Planck Statement○

Kelvin-Planck Statement of the Second Law: It is impossible for any system to operate in a thermodynamic cycle and deliver a new amount of energy by work to its surroundings while receiving energy be heat transfer from a single thermal reservoir

•

Entropy Statement of the Second Law: It is impossible for any system to operate in a way that entropy is destroyed.

•

5.1 Introducing the Second Law

Processes that are spontaneous are irreversible (ie: expansion of a gas/liquid)○

Irreversible Processes: A type of process for which the system and all parts of its surroundings cannot be exactly restored to their respective initial states after the process has occurred

•

Reversible Processes: A type of process for which the system and its surroundings can be returned to their initial states

•

5.3 Irreversible and Reversible Processes

Heat transfer through a finite temperature difference○

Unrestrained expansion of a gas or liquid to a lower pressure○

Spontaneous chemical reaction○

Spontaneous mixing of matter at different compositions or states○

Friction○

Electric current through a resistance○

Magnetization/polarization with hysteresis○

Inelastic deformation○

Such processes generally include one or more of the following irreversibilities•

Internal irreversibilities: irreversibilites that occur within the system○

Note: Internal and external irreversibilities are arbitrarily defined, just as the boundary is arbitrarily defined.

External irreversibilities: irreversibilities that occur within the surroundings○

When analyzing a system for irreversibilities, it is good to divide the irreversibilities into internal irreversibilities and external irreversibilities

•

Irreversible Processes

Reversible processes are idealized-- they do not occur •Reversible Processes

Internally Reversible Process: a process for which there are no irreversibilities within the system•5.3.4 Internally Reversible Processes

○

We can modify the Kelvin-Planck statement for internally reversible processes•5.4 Interpreting the Kelvin-Planck Statement

5.6 Second Law Aspects of Power Cycles Interacting with Two Reservoirs

If were zero, then we would have perfect thermal efficiency. However, this is impossible (Why is this the case?)

○

Consider the thermal efficiency equation:

•

5.6.1 Limit on Thermal Efficiency

Carnot Corollaries•5.6.2 Corollaries of the Second Law for Power Cycles

Chapter 5Thursday, July 12, 2012 2:03 PM

New Section 1

The thermal efficiency of a irreversible power cycle is always less than the thermal efficiency of a reversible power cycle when each operates between the same two thermal reservoirs

1)

All reversible power cycles operating between the same two thermal reservoirs have the same thermal efficiency

2)

Carnot Corollaries•

5.7 Second Law Aspects of Refrigeration and Heat Pump cycles Interacting With Two Reservoirs

Refrigeration Cycle:

○

Heat Pump Cycle:

○

Consider the following coefficients of performance•

Keeping this in mind, if were zero, then that would imply that heat transfer from cold

to hot would be occurring spontaneously-- which is impossible. This would also result in a infinite coefficient of performance. Thus, the coefficient of performance needs to be finite.

○

Remember that both these cycles draw heat from a cold reservoir and put it into a hot reservoir.•

5.7.1 Limits on Coefficients of Performance

The coefficient of performace of an irreversible refrigeration cycle is always less than the coefficient of performance of a reversible refrigeration cycle when each operates between the same two thermal reservoirs

1)

All reversible refrigeration cycles operating between the same two thermal reservoirs have the same coefficient of performance

2)

5.7.2 Corollaries of the Second Law for Refrigeration and Heat Pump Cycles

5.9 Maximum Performance Measures for Cycles Operating Between Two Reservoirs

○

Note: because all processes are irreversible, the no process will actually work at the carnot efficiency

○

Carnot Efficiency: A measure of the thermal efficiency of a reversible cycle operating between two thermal reservoirs

•5.9.1 Power Cycles

○

Refrigeration Cycle•

○

Heat Pump Cycle•

5.9.2 Refrigeration and Heat Pump Cycles

5.10 Carnot Cycle

: Adiabatic compression

•

5.10.1 Carnot Power Cycle

New Section 1

: Adiabatic compression○

: Isothermal expansion while receiving energy from the hot reservoir by heat transfer○

: Adiabatic expansion○

: Isothermal compression while discharging energy to the cold reservoir○

Note: Shaded area represents net work produced per unit mass○

: Isothermal expansion while receiving energy from the cold reservoir via heat transfer○

: Adiabatic compression○

: Isothermal compression while discharging energy to the hot reservoir○

: Adiabatic expansion○

Note: Shaded area represents net work input per unit mass○

•

5.10.2 Carnot Refrigeration and Heat Pump Cycles

Carnot cycle always has 4 internally reversible processes: two adiabatic processes and two isothermal processes

1)

Thermal efficiency of the Carnot power cycle is always given by the equation

.

Don't forget temperature units are to be in Rankine or Kelvin

2)

Coefficients of performance are determined by either

or

. Again,

temperature is in units of Rakine or Kelvin

3)

5.10.3 Carnot Cycle Summary

Version 1:○

: heat transfer at a part of the system boundary□

: absolute temperature□

: no irreversabilities within system

: irreversibiliteis present within system (Because heat is exiting

the system boundary, right?)

: impossible

:□

Version 2:○

Clausius inequality: A statement that applies to any thermodynamic cycle•5.11 Clausius Inequality

New Section 1

6.1 Entropy- A System Property

Entropy is an extensive property. This means entropy depends on the "extent" of the system and only depends on the initial and final states. Path independent.

•

SI:

○

English:

○

Units:•

6.1.1 Defining Entropy Change

○

To obtain a value of entropy, we use the following equation•6.1.2 Evaluating Entropy

Vapor: Use the vapor/superheated tables•

○

○

Saturation Data: Use 2 state tables along with either of the following equations•

○

Liquid Data: We apply the incompressibility rule here to make the following approximation•

6.2 Retrieving Entropy Data

The Tds equations are used for pure, simple compressibility systems undergoing internally reversible processes.

•

○

○

Mass basis○

Mole basis○

Equations•

6.3 Introducing the T ds Equations

○

For an incompressible substance with a constant specific heat•6.4 Entropy Change of an Incompressible Substance

•

•

Remember, •

6.5 Entropy Change of an Ideal Gas

•

6.5.1 Using Ideal Gas Tables

When specific heats are constants, the entropy change equations become the following•6.5.2 Assuming Constant Specific Heats

Chapter 6Friday, July 13, 2012 2:28 PM

New Section 1

○

○

○

○

When energy is removed from a system, the entropy of the system decreases. When energy is transferred into a system, the entropy of the system increases.

•

Isentropic Process: A constant-entropy process•

6.6 Entropy Change in Internally Reversible Processes of Closed Systems

○

The area under a temperature, entropy graph is equal to the change in heat•6.6.1 Area Representation of Heat Transfer

Entropy change equals entropy transfer plus entropy production○

•

○

Recall, •

Positive: System becomes more disorderly○

Negative: System becomes more orderly○

Zero: System is in same amount of disorder○

However, change in entropy can be positive, negative, or zero•

○

Entropy Rate Balance•

6.7 Entropy Balance for Closed Systems

Increase of Entropy Principle: •6.8 Directionality of a Process

•

Rate of Energy Transfer equals rate of entropy transfer via mass flowing in plus rate of entropy transfer via mass flowing out plus rate of entropy production

•

6.9 Entropy rate Balance for Control Volumes

Steady State Entropy Rate Balance:

•

One Inlet/Outlet:

•

6.10 Rate Balances for Control Volumes at Steady State

Isentropic: A process with constant entropy•

○

For an isentropic process,•

○

For isentropic (no change in entropy) processes involving air, the following equations can be applied

•

6.11 Isentropic Processes

New Section 1

○

○

○

If the gas constant is constant for the two states of an idea gases, the following equations apply•

Isentropic Turbine Efficiency:

○

○

Turbines•

Isentropic Nozzle Efficiency:

○

○

Nozzles•

Compressors/Pumps•

6.12 Isentropic Efficiencies of Turbines, Nozzles, Compressors, and Pumps

New Section 1

Isentropic Compressor/Pump Efficiency

○

Compressors/Pumps•

Heat○

Constant □

Steady state□

For polytropic processes, obtain value from

Work○

For an isothermal and internally reversible process,•6.13 Heat Transfer and Work in Internally reversible, Steady-State Flow Processes

New Section 1

Exergy can be transferred to and from a system○

Exergy is a quantity that quantifies potential for use. Exergy is not conserved, but rather destroyed by irreversibilities.

•7.1 Introducing Exergy

Work can be harvested when two systems at different states are brought together○

Work can be harvested as two systems approach equilibrium○

Two important concepts:•

The book considers the environment to be a compressible system that is large and at a uniform temperature ( ) and pressure ( )

○

Environment: The surroundings of the system of inquiry•

Dead State: When a system is in equilibrium with the environment; temperature and pressure

•

Exergy: Exergy is the maximum theoretical work obtainable from an overall system consisting of a system and the environment as the system comes into equilibrium with the environment (passes to the dead state)

•

7.2 Conceptualizing Exergy

Units of exergy are the same as units of energy

○

The exergy of a system is given by the following equation•

Exergy is a measure of the departure of the state of a system from that of the environment. It is therefore an attribute of the system and environment together. However, once the environment is specified, a value can be assigned to exergy in terms of property values for the system only, so exergy can be regarded as a property of the system. Exergy is an extensive property

1)

The value of exergy cannot be negative. The minimum value of exergy is zero, which corresponds to a system being at the dead state.

2)

Exergy is not conserved, but it is destroyed by irreversibilities. A limiting case is when exergy is completely destroyed, as would occur if a system were permitted to undergo a spontaneous change to the dead state with no provision to obtain work

3)

Exergy has been viewed thus far as the maximum theoretial work obtainable from an overall system of system plu senvironment as the system passes from a given state to the dead state. Alternatively, exergy can be regarded as the magnitude of the minimum thoeretical work input required to bring the system from the dead state to the given state.

4)

When a system is at the dead state, it is in thermal and mechanical equilibrium with the environment, and the value of exergy is zero. More precisely , the thermomechanical contribution to exergy is zero.

5)

5 Important aspects of exergy•

○

Specific Exergy •

Note: Dead states are not required to calculate exergy change

○

Exergy Change•

7.3 Exergy of a System

Closed System Exergy Balance•7.4 Closed System Exergy Balance

Chapter 7Sunday, July 29, 2012 9:18 AM

New Section 1

Exergy change = Exergy transfers - Exergy Destruction

○

Exergy transfer accompanying heat transfer○

Exergy transfer accompanying work○

□

Destruction of Exergy○

○

Exergy change can be positive, negative, or zero○

Alternative form of Closed System Exergy Balance•

The change in exergy for an isolated system can only be negative, as exergy can only be destroyed

•

○

Steady State form:○

Rate of exergy transfer accompanying heat transfer○

Closed System Exergy Rate Balance•

○

Steady State Exergy Rate Balance•

○

Specific Flow Exergy•

○

Alternative, more compact form•

I don’t understand the term

○

○

One inlet/outlet•

7.5 Exergy Rate Balance for Control Volumes at Steady State

Exergetic Efficiency: An evaluation of the effectiveness of energy resource utilization•7.6 Exergetic Efficiency

New Section 1

Source temperature

: Use Temperature

: Dead State Temperature

○

Refer to page 393 & 394○

Exergetic efficiency of specific components•

New Section 1

8.2 The Rankine Cycle

Turbine:○

Condenser: ○

Pump:○

Boiler:○

Note: Careful how the

term is defined. The book has it such that this is a

positive value, when according to accepted sign notation,

would be negative

□

Thermal Efficiency: ○

Heat rate: The amount of energy added by heat transfer to the cycle○

Back Work Ratio (bwr): ratio of the pump work input to the work developed by the turbine○

•

Modeling the Rankine Cycle through Power Plant Analysis

The Ideal Rankine Cycle

Chapter 8Sunday, August 12, 2012 10:47 PM

New Section 1

: Isentropic expansion of working fluid through turbine from saturated vapor at state 1 to the condenser pressure

○

: Heat transfer from the working fluid as it flows at constant pressure through the condenser with saturated liquid at state 3

○

: Isentropic compression in the pump to state 4 in the compressed liquid region○

: Heat transfer to the working fluid as it flows at constant pressure through the boiler to complete the cycle

○

Note: represent the process that results from superheating state ○

Processes:•

Area represented by represents the heat transfer to the working fluid passing through the boiler

•

Area represents the heat transfer from the working fluid passing through the condenser

•

Area represents the net work output•

The subscript s denotes that the process is isentropic (internally reversible and adiabatic)

○

Work done by the pump•

Increasing boiler pressure of the ideal Rankine cycle increases thermal efficiency•Decreasing condenser pressure of the ideal Rankine cycle increases thermal efficiency•

Effects of Boiler and Condenser Pressures on the Rankine Cycle

While the Carnot cycle has greater thermal efficiency, the Carnot cycle deals with two phase liquids. These are not practical to work with in a power plant

•Carnot vs Rankine

When the working fluid travels through the turbine, it expands. This is the principle loss of turbines. An efficiency variable is used to describe the isentropic turbine efficiency

Turbine○

Internal effects•Irreversibilities and Losses of the Carnot Cycle

New Section 1

□

□

Similarly, there is an isentropic efficiency for the pump

□

Alternatively,

Pump○

Friction reduces pressure

Miscellaneous Effects○

A major source of irreversibility is combustion and heat loss to the surroundings○

Stray heat transfers also contribute to irreversibility ○

External Effects•

While altering boiler and condenser pressure will improve thermal efficiency, it decreases the quality of the working fluid. This can have a detrimental effect on the turbine/other working parts. Generally, power plants try to keep the quality above 90%

•8.3 Improving Performance- Superheat, Reheat, and Supercritical

This process allows power plants to avoid problems with low quality○

This process involves heating the saturated vapor at the turbine inlet to a supercritical state. •Superheat

There are two turbine stages. After the steam exits the first stage, it is reheated before entering a second stage

•Reheat

This means that water can be converted to steam without a pronounced phase change(Is this correct?)

○

This process involves heating water above its critical pressure•

Supercritical power plants have higher upfront costs, but cheaper to fuel because they are more thermally efficient

•

Supercritical

Regeneration: Has the effect of increasing the average temperature of heat addition, thus increasing thermal efficiency

•8.4 Improving Performance -- Regenerative Vapor Power Cycle

Streams of different temperatures mix to for a single stream at an intermediate temperature•Open Feedwater Heaters

New Section 1

After steam enters the first turbine, some of the steam is bled out to the open feedwater heater•Now, heat addition from fossil fuels is only necessary from •While open feedwater heating produces less work, the reduction in heat added offsets the decrease in net work, thus making these power plants more effective

•

Where is the fraction of the total mass flow rate flowing into the open feedwater heater

○

Mass flow rate of working fluid into open feedwater heater from turbine•

Closed Feedwater Heaters

New Section 1

Because fluids are isolated, they can be at different pressures○

Shell-and-tube-type recuperators in which the feedwater temperature increases as the extracted steam condenses o the outside of the tubes carying the feedwater.

•

Condensate within the closed feedwater heater can be removed via pump or trap•

○

Fraction of mass flow rate of working fluid that is bled into the closed feedwater heater•

Power plants often have multiple combinations of open and closed feedwater heaters. •

This process of venting dissolved gasses is known as deaeration○

Generally, these plans have atleast one open feedwater heater operating at a pressure greater than atmospheric pressure. This allows for dissolved gasses to be vented fro the cycle.

•

Multiple Feedwater Heaters

8.5 Other Vapor Power Cycle Aspects

The most popular is demineralized water because it is plentiful, cheap, nontoxic, chemically stable, and relatively noncorrosive

•

A difficulty with water is its high critical pressure. This makes it difficult to design supercritical power plants that rely on water

•

Working Fluids

These usehydrogarbosn and common refrigerants such as ammonia and silicon oil•Organic Rankine Cycles

Couples two vapor cycles so the energy discharged by heat transfer from one cycle is the input for the other

•

There are usually two working fluids in such cycles to maximize usage of the heat discharge•

Binary Vapor Cycle

Cogeneration: Power plants that yield both electricity and steam•District Heating: Heating plants within communities that serve to provide steam for heating and electricity for appliance use

•

Cogeneration

New Section 1

○

Diagram of a piston in an engine•

Compression Ratio: The volume of the piston at bottom dead center divided yb the volume of the piston at top dead center.

•

General Engine cycle on a P-V graph•

9.1 Introducing Engine

Chapter 9Saturday, August 18, 2012 11:15 AM

New Section 1

○

Intake Stroke: The intake valve is open and the piston draws a fresh charge into the cylinder. For spark-ignition engines, this charge is a combustible mixture of air and fuel. For compression-ignition engines, this charge is air.

1)

Compression Stroke: This stroke requires work. Both valves are closed and the piston decreases the volume of the chamber to create a high pressure, high temperature gas mixture. For spark-ignition engines, combustion is induced near the end of the compression stroke by the spark plug. In compression-ignition engines, the combustion is initiated by injecting fuel into the hot compressed air

2)

Power Stroke: With combustion, the gas mixture expands and the engine produces work as the piston returns to bottom dead center

3)

Exhaust Stroke: The burned gasses are purged form the cylinder through the open exhaust valve

4)

Engine cycle for a 4 stroke engine•

Note: Engines undergo mechanical cycles, not thermodynamic cycles. Matter is injected and also flushed out.

•

○

Mean Effective Pressure: The theoretical constant pressure, that if acted on the piston during a power stroke, would produce the same net work as actually developed in one cycle

•

Fixed amount of air modeled as an ideal gas is the working fluid○

The combustion process is replaced by a heat transfer from an external source○

There are no exhaust and intake processes. The cycle is completed by a constant-volume heat transfer process taking place while the piston is at the bottom head center position

○

All processes are internally reversible○

Air-Standard Analysis: A simplified analysis of internal combustion engines that involves the following elements

•

Cold Air-Standard Analysis: The specific heats are assumed to be the same as their ambient •

New Section 1

Cold Air-Standard Analysis: The specific heats are assumed to be the same as their ambient temperature values

•

○

P-v & T-S diagrams•

:Isentropic compression of air as piston moves from bottom to top dead center○

: Constant volume heat transfer to the air from an external heat source while the piston is at top dead center. (This is an easier way to analyze the process of combustion

○

: Isentropic expansion○

: Constant volume process in which heat is rejected from the air while the piston is at bottom dead center.

○

Processes•

: Heat added per unit mass

: Heat rejected per unit mass

T-s Graph○

: Work input per unit mass during compression

: Work output per unit mass during expansion

P-v Graph○

Graph Interpretation:•

In the Otto cycle, there are two processes that only involve work and two that only involve heat transfer

○

The work cycle can also be expressed as net heat added□

CycleValue Computations (Note: this is not typical sign convention‼)○

Thermal Efficiency○

Isentropic processes ○

Cycle Analysis•

9.2 Air-Standard Otto Cycle

New Section 1

Compression Ratio:

□


□

When the Otto cycle is analyzed using the Cold Air Standard Analysis, the following equations can be used instead of the above two and equations

○

This shows that it is advantageous for engines to have high compression ratios. But engine knock/auto ignition places an upper limit on compression ratios

○

Thermal efficiency for a cold-air standard basis•

9.3 Air-Standard Diesel Cycle

: Isentropic compression; heat is transferred into the working fluid at constant pressure

○

: First part of the power stroke○

: Remainder of power stroke○

: heat is rejected from the air while piston is at dead center (Shortcut to having to deal with air intake and exhaust output)

○

Processes•

: Heat added per unit mass

: Heat rejected per unit of mass

T-s Diagram○

: Work input per unit of mass

: Work done per unit of mass

P-v Diagram○

P-v and T-s Graph interpretation•

○

○

○

Cycle Analysis•

Thermal Efficiency•

New Section 1

○

Compression Ratio:

○

Cuttoff Ratio:

○

○

○

Fixing States•

○

○

○

Cold Air Standard Analysis•

New Section 1

Chapter 1

○

Kelvin (SI) vs Rankine(English) Scale•

○

Celsius vs Kelvin•

○

Fahrenheit vs Rankine•

○

Fahrenheit vs Celcius•

Temperature Conversions

: Density of substance○

: Choose accordingly. Remember pressure increases as height decreases○

•

Force equals the product of pressure and area○

•

Pressure Calculations

: system is doing work to surroundings○

: surroundings are doing work on system○

Work•

: Heat is entering the system○

: Heat is leaving the system○

Heat•

Sign Notation

Power is the product of force and velocity, or the rate at which work is being done.

○

•

Power

•

Work via Compression

Chapter 2

•

•

Total Energy / Total Energy Change

Page 56•Modes of Heat Transfer (Conduction, Radiation, Convection)

•

•

○

After a full rotation of a cyclic process, the substance returns to its original state. thus . Therefore,

•

Conservation of Energy / Energy Rate Balance

•

Closed System Energy Balance

Compiled InformationThursday, July 26, 2012 11:10 AM

New Section 1

•

•

Internally Reversible Cycles

•

○

Thermal Efficiency•

Power Cycles

•

Refrigeration Cycle: ○

Heat Pump Cycles:○

Coefficients of Performance (Bigger is better)•

Refrigeration & Heat Pump Cycles

Chapter 3

•

Quality

•

Average Specific Volume

•Enthalpy

○

u ○

○

○

Approximating specific volume, internal energy, and enthalpy•

○

Liquid/Metal Specific heats•

○

○

Change in specific internal energy and enthalpy•

Incompressible Substances (Liquids and Solids)

•

Unit-less Compressibility Factor

○

○

○

○

Specific Heats•

Change in specific internal energy; Varying specific heat•

Ideal Gasses

New Section 1

○

Change in specific internal energy; Varying specific heat•

○

Change in specific internal energy; Constant specific heat•

○

Change in specific enthalpy; Varying specific heat•

○

Change in specific enthalpy; Constant specific heat•

: molar volume

○

○

•

: specific volume○

, where is the same as above and is the molar mass○

•

: Volume○

○

: Mass of gas○

•

Helpful Ideal Gas Equations

Chapter 4

: Density of substance○

: Cross sectional area○

: Velocity of substance○

: Specific volume○

•

Mass Flow Rate

○

General Equation•

○

Steady State•

Conservation of Mass Flow in a Control Volume

○

General equation•

○

Steady State •

Conservation of Energy in a Control Volume

○

Turbine (Produces Work)•

○

Compressors & Pumps (Receives Work)•

Heat Exchangers (Generally involves two substances)•

Different Types of Control Volume Systems

New Section 1

○

○

Throttling Devices: Do nothing. Just control mass flow rate•

○

Mass Balance•

○

Energy Balance•

Transient Analysis

Chapter 5

: Impossible

: No irreversibilities

: Irreversibilities present

○

•

Entropy Production (Exchange of heat over a boundary at temp )

Refer to Chapter 5 Detailed Notes•Carnot Power Cycles

Chapter 6

○

○

General equations (Can be rewritten with specific internal energies, enthalpies, and entropies)

•

○

Incompressible Substances•

○

○

Ideal Gasses; Varying specific heats•

○

○

Ideal Gasses; Constant specific heats•

○

Reference Values (Only applies to a handful of gasses)•

Tds Equations

•

Heat Transfer & Entropy Change

Entropy Balance / Rate Balance Closed Systems

New Section 1

: Entropy transfer across system boundary○

values are restricted to positive (Irreversibilities present) and (Reversible process)

○

can be positive (more disorder), negative (more order), 0 (no change in disorder)

○

•

•

•Principle of Increasing Entropy

○

General Equation•

○

Steady State•

Entropy Rate Balance For Control Volumes

•

•

Isentropic Processes Involving Air

•

•

Ideal Gas with Constant Specific heat

See Chapter 6 Notes•Isentropic Efficiencies

○

Heat•

○

Work•

Isothermal & Internally Reversible Processes

Chapter 7

are properties of the dead state○

•Exergy of a System Relative to Dead State

•

Specific Exergy of a System Relative to Dead State

•Change in Exergy between Two States

: Change in exergy between two states

•Closed System Exergy Balance

New Section 1

: Change in exergy between two states○

: Change in exergy as a result of heat transfer○

: Change in exergy as a result of work done on/by system○

Positive: irreversibilities are present within system□

Zero: No irreversibilities are present within system□

There are two possible values of

: Destruction of exergy○

○

General Equation (NOT STEADY STATE)•

○

Steady State Form

•

Closed System Exergy Rate Balance

□

: Heat transferred into system

: Work on/by system

□

: Exergy Flow into system

□

L Exergy flow out of system

: Exergy destruction

○

Rate Balance•

○

Specific flow exergy •

Exergy Rate Balance for Control Volume at Steady State

○

: Rate of heat use○

: Use temperature○

: Rate of heat delivery from source○

: Source temperature○

•

Exergetic Efficiency

Chapter 8Rankine Cycle

New Section 1

Turbine:

•

Condenser:

•

Pump:

•

Boiler:

•

Thermal Efficiency:

•

Turbines:

○

Pump:

○

Isentropic Efficiencies•

Chapter 9

Air-Standard Analysis of The Otto Cycle

○

Compression Ratio:

○

Fixing States for Air Standard Analysis•

○

○

Compression Ratio:


Thermal Efficiency Shortcut for CASA:

○

Fixing States Cold Air Standard Analysis (Note: Can't use values for CASA)•

Work In:

Work:○

Cycle Analysis (DON'T STRAY FROM SIGN CONVENTION)•

New Section 1

Work In:

Work Out:

Heat In:

Heat Out:

Heat:○

Thermal Efficiency○

Air-Standard Diesel Cycle

○

○

Compression Ratio:

Cuttoff Ratio:

○

Fixing States for Air Standard Analysis•

○

○

Thermal Efficiency:

○

Fixing States with Cold Air Standard Analysis (Note: Can't use values for CASA)•

○

○

○

○

Thermal Efficiency:

○

Cycle Analysis •

First Law of Thermodynamics: Energy is conserved1)Second Law of Thermodynamics: Systems tend to naturally approach equilibrium; Heat is naturally transferred from a hot to a cold reservoir

2)

Carnot Corollaries3)

Important Terms

New Section 1

The thermal efficiency of an irreversible cycle is always less than the thermal efficiency of a reversible power cycle

a.

All reversible power cycles operating between the same two thermal reservoirs have the same thermal efficiency

b.

Carnot Corollaries3)

Isometric: Constant Volume4)Isentropic: Constant Entropy5)Isothermal: No temperature change6)Isobaric: No pressure change7)Adiabatic: No heat exchange (Synonymous to isentropic)8)

New Section 1

Energy is conserved: •First Law of Thermodynamics

Entropy cannot be destroyed•

If something happens spontaneously, entropy increases○

Entropy Increases•

Energy runs downhill•

Second Law of Thermodynamics

Important TheoryFriday, August 24, 2012 2:12 PM

New Section 1

NOTHING•How In-wheel Motors Work

Fuel Cells operate 60-80 degrees Celcius1.

This is rarely the case as the hydrogen is usually not so pure. So bump off another 65%

a.Fuel cells can be, at best, 80% efficient if working with pure hydrogen2.

Passing power through gears, axles, etc.a.Generous approximation for motor to wheel power transmission: 80%3.

Hydrogen generation requires input of energy from other power sources4.Efficiency of a gasoline car: 20%5.Fuel Cells are expensive because the contain rare earth metals such as

platinum6.

Car operation in different temperatures is yet to be stable7.

How Fuel Cells Work

Process is estimated to be 50% efficienta.Electrolysis: Process of splitting water into hydrogen and oxygen1)

Cars would need large storage tanks holding potentially explosive and thus dangers gases (hydrogen and oxygen)

a.

Fuel cells cannot rapidly deliver electrical energy to the motorb.Makes no sense to use fossil fuels to generate energy for the production of fuel cells.

c.

Problems with hydrogen cars2)

Hydrogen Cars

Process of electrolysis requires 1.23 Volts per cell1)

This means 50% efficiency in the creation of fuel cellsa.On average, fuel cells that are produced have returns of .75 volts/cell2)

Immediately, some of the energy is lost to powering onboard electronics/pumps/etc that are not related to driving: 10%

3)

Process of creating hydrogen: Transportation via fuel lines and truck transport: take away an estimated 10%

4)

Efficiency of Hydrogen Fuel Cell, Diesel-SOFC-Hybrid and Battery Electric Vehicles

Process of creating hydrogen

○

Using hydrogen to power carsPollution reduction

○

Does producing hydrogen cells really reduce pollution?

○

Efficiency•

Feasability•

Topics:

1 Page AnalysisSunday, July 29, 2012 9:14 PM

New Section 1

thermodynamics

Documents

system boundaries1

system boundarieswhy

systemsclosed system

system boundary1

type of closed system

closed systemclosed

open systemopen system

chemicalequilibrium