9.4: Supplementary Materials- Course Learning Objectives

Introduction, Basic Concepts, and Appendices A and B

1. Define, illustrate, compare and contrast the following terms and concepts:
   • engineering analysis vs. engineering design
   • algorithm vs. heuristic
   • model (as discussed in the notes)
     
   • system
     • surroundings
     • boundary (control surface)
     • closed system (control mass) vs. open system (control volume)
     • interactions between a system and its surroundings
     • isolated system
   • property
     • extensive vs. intensive
     • necessary and sufficient test for a property
   • state
   • process
     • cycle
     • steady-state system
       • finite-time process
       • transient
         
   • units and dimensions
     • primary vs. secondary dimensions
     • base units and derived units
     • unit conversion factor
   • weight and mass
     • molar mass (molecular weight)
     • amount of substance — mole (\(\mathrm{mol}\), \(\mathrm{kmol}\), \(\mathrm{lbmol}\), \(\mathrm{slugmol}\), etc.)
     • local gravitational field strength (standard values)
       • \(g = 9.80665 \mathrm{~N}/\mathrm{kg} = 1.0000 \mathrm{~lb}_{\mathrm{f}} / \mathrm{lb}_{\mathrm{m}} = 32.174 \mathrm{~lb}_{\mathrm{f}} /\mathrm{slug}\)
       • relationship to local gravitational acceleration: \(g = 9.80665 \mathrm{~m}/\mathrm{s}^{2} = 32.174 \mathrm{~ft}/\mathrm{s}^{2}\)
     • slug vs. pound-mass (\(\mathrm{lb}_{\mathrm{m}}\) or \(\mathrm{lbm}\)) vs pound-force (\(\mathrm{lb}_{\mathrm{f}}\) or \(\mathrm{lbf}\))
       
   • continuum hypothesis
     • macroscopic vs. microscopic viewpoint
       
   • accounting concept
     • basic components
       • accumulation within the system
       • transport across system boundary
       • generation/consumption (production/destruction) within the system
         
   • finite-time vs. rate form
     • rate of accumulation (“rate of change”) vs. accumulation (“change in”)
     • transport rate vs. amount transported
     • generation (consumption) rate vs. amount generated (consumed)
       • conserved property vs. non-conserved property
   • conservation laws vs. accounting statements (balances)
2. Given a sufficient set of unit conversion factors, convert the numerical value of a physical quantity from one set of units to a different, specified set of units.
3. Explain in words the difference between the mass of an object and its weight. Demonstrate this understanding by applying the defining equation for weight, \(W = mg\), and Newton’s second law, \(F = ma\) to solve problems involving weight, mass, and acceleration. Answers for mass, weigh, and acceleration must be given with appropriate and standard units.
4. List the seven components of the problem solving format (methodology for engineering problem solving), explain the significance of each part, and use the format correctly in your problem solutions.
5. Given a problem that can be solved by accounting for physical quantities or, if you are requested to use the accounting principle, apply the accounting principle to solve for the desired information. Be sure to clearly indicate the system of interest, the property (or stuff) to be counted, and the time period of interest. Problems should be worked showing sufficient steps so that the method used is clear.
6. Give both a written and a symbolic statement of the rate form of the accounting principle and the finite-time form of the accounting principle. Clearly indicate the accumulation, transport, and generation terms.
7. Explain the mathematical and the physical difference between the "rate of accumulation (or change)" term and the "transport rate" and "generation/consumption rate" terms in the rate form of the accounting principle. For example, what happens when you integrate a rate of change term as compared to integrating a transport term, e.g. \(d m_{s y s} / d t\) vs. \(\dot{m}\).
8. Given a list of physical quantities, determine which of them are properties and indicate whether they are intensive or extensive properties. Explain how you made your decisions.

Chapter 3 — Conservation of Mass and Chemical Species Accounting

1. Define, illustrate, compare and contrast the following terms and concepts:
   • Mass
     • mass vs. weight
     • units of measurement
       • mass: \(m \ (\text{kg, g, lbm, slug})\)
       • amount of substance: \(n \ (\text{kmol, gmol, lbmol, slugmol})\); (most useful when chemical reactions are involved)
     • molecular weight (molecular mass): \(M \ (\mathrm{kg} / \mathrm{kmol}, \mathrm{~g} / \mathrm{gmol}, \mathrm{~lbm} / \mathrm{lbmol})\)
       • ​​​​​relationship between \(m\) and \(n\)
       • density & specific volume (how are they related?)
       • specific weight vs. specific gravity (how are they different?)
         
   • Application of Accounting Principle for Mass
     • rate of accumulation of mass within the system
     • amount of mass within the system: \(\boxed{m_{sys}=\iiint\limits_{V} \rho \ dV}\)
       • density vs. specific volume \((\rho\) vs \(v)\)
     • transport rate of mass across system boundaries
       • mass flow rate: \(\boxed{\dot{m} = \iint\limits_{A_{c}} \rho V_{n} \ dA} \quad (\mathrm{kg} / \mathrm{s}, \mathrm{~lbm} / \mathrm{s})\)
       • volumetric flow rate: \(\dot{V\kern-0.9em\raise0.3ex-} = \iint\limits_{A_{c}} V_{n} \ dA\) where \(A_{c}=\) cross-sectional area \(\left(\mathrm{m}^{3} \ \mathrm{s}, \mathrm{~ft}^{3} / \mathrm{s}\right)\)
       • molar flow rate : \(\dot{n}=\dot{m} / M \quad (\mathrm{kmol} / \mathrm{s}, \mathrm{~mol} / \mathrm{s}, \mathrm{~lbmol} / \mathrm{s})\)
       • local normal velocity: \(V_{n}\)
       • one-dimensional flow assumption
       • average velocity at a cross-section: \(V_{AVG}\)
         • mass and volumetric flow rate based on average velocity: \[\dot{m} = \rho A_{c} V_{AVG} \quad \text{&} \quad \dot{V} = A_{c} \mathrm{V}_{AVG} \nonumber \]
     • generation/consumption rate of mass within the system
       • Empirical result ..... Mass is conserved! It’s really a conservation principle!
   • Conservation of mass equation: \[ \begin{array}{ll} \displaystyle &\mathbf{rate \ form} \quad\quad &\frac{d m_{sys}}{dt} = \sum \dot{m}_{\text{in}} - \sum \dot{m}_{\text{out}} \\ \displaystyle &\mathbf{finite} \text{-} \mathbf{time \ form} & m_{\text{sys, final}} - m_{\text{sys, initial}} = \sum m_{\text{in}} - \sum m_{\text{out}} \end{array} \nonumber \]
     
   • Chemical Species (Compounds)
     • units of measurement --- same as for mass
       • \(m_{i}=\) mass of component \(i\)
       • \(n_{i}=\) moles of component \(i; \quad n_{i}=m_{i} / M_{i}\)
     • mixture composition \[\begin{aligned} &\text{moles of mixture: } \quad \boxed{n = \sum_{i=1}^{N} n_{i}} \quad \text{ where } N= \text{number of components in the mixture} \\ &\text{mole fractions: } \quad n f_{i} = \frac{n_{i}}{n_{\text{mix}}} \text{ and } \boxed{\sum_{i=1}^{N} n f_{i} = 1} \\ &\text{mass of mixture: } \quad \boxed{m = \sum_{i=1}^{N} m_{i}} \\ &\text{mass (weight) fractions: } \quad m f_{i} = \frac{m_{i}}{m_{\text{mix}}} \text{ and } \boxed{\sum_{i=1}^{N} m f_{i}=1} \end{aligned} \nonumber \]
   • Application of Accounting Principle for Chemical Species
     • rate of accumulation of component \(i\) within the system
       • amount of component \(i\) within the system: \[m_{i, \ sys} = \iiint\limits_{V} \rho_{i} \ dV \quad \text { and } \quad n_{i, \ sys} = \frac{m_{i, \ sys}}{M_{i}} \nonumber \]
       • transport rate of component \(i\) across system boundaries
         • mass flow rate of component \(i\): \dot{m}_{i} \quad (\mathrm{kg} / \mathrm{s}, \mathrm{~lbm} / \mathrm{s}, \mathrm{~slug} / \mathrm{s})\)
         • molar flow rate of component \(i\): \dot{n}_{i} \quad (\mathrm{kmol} / \mathrm{s}, \mathrm{~mol} / \mathrm{s}, \mathrm{~lbmol} / \mathrm{s})\)
       • generation/consumption rate of species \(i\) within the system
         • chemical reactions and generation/consumption
           • balanced reaction equations and consumption/generation terms
         • generation (production or creation) rate: \(\quad \dot{m}_{i, \text{ gen}}\) or \(\dot{n}_{i, \text{ gen}}\)
         • consumption (destruction) rate: \(\quad \dot{m}_{i, \text { cons}}\) or \(\dot{n}_{i, \text { cons}}\)
   • chemical species accounting equation (mass basis) \[\begin{aligned} & \mathbf{rate \ form} \quad \frac{dm_{i, \ sys}}{dt} = \sum \dot{m}_{i, \text { in}}-\sum \dot{m}_{i, \text { out}} + \dot{m}_{i, \text { gen}}-\dot{m}_{i, \text { cons}} \\ & \mathbf{finite} \text{-} \mathbf{time \ form} \quad m_{i, \text{ sys, final}} - m_{i, \text{ sys, initial}} = \sum_{\text{in}} m_{i, i} - \sum_{\text{out}} m_{i, e} + m_{i, \text{ gen}} - m_{i, \text{ cons}} \end{aligned} \nonumber \]
   • chemical species accounting equation (mole basis) \[\begin{aligned} &\mathbf{rate \ form} \quad \frac{d n_{i, \ sys}}{dt} = \sum n_{i, \text{ in}} - \sum \dot{n}_{i, \text{ out}} + \dot{n}_{i, \text{ gen}} - \dot{n}_{i, \text{ cons}} \\ &\mathbf{finite} \text{-} \mathbf{time \ form} \quad n_{i, \text {sys, final}} - n_{i, \text{ sys, initial}} = \sum n_{i, \text{ in}} - \sum n_{i, \text{ out}} + \mathrm{n}_{i, \text{ gen}} - \mathrm{n}_{i, \text{ cons}} \end{aligned} \nonumber \]
   • Constitutive relation
     • Examples: Ohm’s Law, Ideal Gas Model
   • Ideal Gas Model
     • universal gas constant \(R_{u}\) vs. specific gas constant \(R\)
2. Given one of the species accounting or conservation of mass equations and a list of assumptions, carefully indicate the consequences of each assumption. Typical assumptions include: steady-state, one-inlet/one-outlet, closed system, open system, and no chemical reactions.
3. Given one of the species accounting or conservation of mass equations, explain what each term represents physically and how it relates to the overall accounting framework discussed in Chapters 1 and 2.
4. Given information about the local velocity distribution and density distribution at the boundary of a system, calculate the mass flow rate and the volumetric flow rate at the boundary.
5. Given a mixture composition in terms of either mass (weight) fractions or mole fractions, determine the composition in the other measure. If total mass of the mixture is specified, determine the moles or kilograms of each component in the mixture. (Best done using a simple table format.)
6. Given a problem that can be solved using conservation of mass and species accounting, you should be able to do the following tasks:
   1. Select an appropriate system. Identify the system and its boundaries on an appropriate drawing. Describe the system and its boundaries in sufficient detail so that there is no confusion about your choice. Indicate whether the system is open or closed.
   2. Indicate the time interval appropriate for the problem (e.g. should you use the rate form or the finite-time form?).
   3. Clearly identify and count the number of unknowns you are trying to find. Define and use a unique symbol for each unknown.
   4. Develop a set of INDEPENDENT equations that are equal in number to the number of unknowns and are sufficient to solve for the unknowns. These equations are developed using conservation of mass, species accounting, and information given in the problem statement, e.g. physical constraints and constitutive equations.
   5. Solve for the unknown quantities.
   6. Substitute in the numerical values to find a numerical answer.
7. Given a problem with non-uniform chemical composition, i.e. a separation, distillation or a mixing problem, apply conservation of mass and species accounting to solve for the unknown mass flow rates or masses and mixture compositions.
8. Given a numerical value for one of the following quantities, determine the numerical value of the remaining quantities: density, specific volume, specific weight, specific gravity
9. Given any two of the following properties—pressure, temperature, and density (mass or molar)—use the ideal gas equation to find the unknown property.

Chapter 5 — Conservation of Linear Momentum

1. Define, explain, compare and contrast the following terms and concepts:
   • Particle vs. Extended Body
     • Rigid body
   • Kinematic relationships: position, velocity, and acceleration
   • Linear Momentum
     • linear momentum of a particle: \(\mathbf{P}=m \mathbf{V}\)
       • specific linear momentum: \(\vec{V}\)
       • units of linear momentum \((\mathrm{N} \cdot \mathrm{s} ; \mathrm{~lbf} \cdot \mathrm{s})\)
     • vector nature of linear momentum
     • inertial reference frame
   • Application of Accounting Principle for Linear Momentum
     • amount of linear momentum within the system: \(\mathbf{P}_{sys} = \displaystyle \int\limits_{V\kern-0.5em\raise0.3ex-_{sys}} \mathbf{V} \rho \ d V\kern-0.8em\raise0.3ex-\)
     • transport rate of linear momentum across the system boundaries
       • external forces: \(\displaystyle \sum \mathbf{F}_{\text{external}}\)
       • body forces
       • surface (contact) forces
         • normal stress vs. shear stress
       • mass transport of linear momentum: \(\displaystyle \sum_{\text {in}} \dot{m}_{i} \mathbf{V}_{i} - \sum_{\text {out}} \dot{m}_{e} \mathbf{V}_{e}\)
     • generation/consumption rate of linear momentum within the system
       • Empirical result ----- Linear momentum is conserved!
   • Conservation of Linear Momentum Equation
     • rate form \(\quad \displaystyle \frac{d\mathbf{P}_{\text {sys}}}{dt} = \sum \mathbf{F}_{\text {external}} + \sum_{\text {in}} \dot{m}_{i} \mathbf{V}_{i}-\sum_{\text {out}} \dot{m}_{e} \mathbf{V}_{e}\)
   • Impulse: \(\quad \mathbf{I} = \displaystyle \int\limits_{t_{1}}^{t_{2}} \mathbf{F} \ dt\)
   • Impulsive Force: \(\quad \mathbf{F}_{\text {avg}} = \displaystyle \frac{\mathbf{I}}{\Delta t} = \frac{1}{\Delta t} \int\limits_{t}^{t + \Delta t} \mathbf{F} \ dt\)
   • Conservation of Linear Momentum and Newton’s Laws
   • Center of mass
   • Dry Friction (A useful constitutive relation)
     • static friction coefficient
     • kinetic (sliding) friction
   • Relative velocity
2. Given a problem that can be solved using conservation of linear momentum, you should be able to do the following:
   1. Select an appropriate system that can be used to find the requested unknowns using the information given in the problem.
      • Clearly identify the system and its boundaries on an appropriate drawing.
      • Carefully label all transports of linear momentum with the surroundings. (This is commonly called a free-body diagram.)
   2. Indicate the time interval appropriate for the problem.
   3. Clearly identify and count the number of unknowns you are trying to find. Define and use a unique symbol for each unknown.
   4. Develop a set of INDEPENDENT equations that are equal in number to the number of unknowns and are sufficient to solve for the unknowns. These equations are developed using the conservation and accounting equations and the information given in the problem. Carefully indicate how the given information plus your assumptions are used to develop the problem-specific equations from the general accounting and conservation principles. (Recognize that in a two-dimensional problem, application of conservation of linear and angular momentum to a system can contribute at most three independent equations.)
   5. Solve for the unknown values.
3. Starting with the conservation of linear momentum equation, show what assumptions are necessary to develop the traditional result for a rigid body: \(\mathbf{F} = m \mathbf{a}\).
4. Given information about the acceleration of an object as a function of time, use elementary calculus to develop an equation for the velocity and as a function of time.
5. Given information about the velocity of an object as a function of time, use elementary calculus to develop an equation for the position as a function of time.
6. Use the concepts embodied in the conservation of momentum equation, including transport and storage of linear momentum, to explain the behavior of a device or system.
7. Given a problem that involves friction, use both sliding and static friction forces where appropriate to explain the motion and/or forces in the system.
8. Given a problem with impulsive forces or loads, evaluate the impulse applied to the system, and if the time interval is known, determine the average value of the impulsive force over the time interval.
9. Given a problem where relative velocities are given or required, correctly convert relative velocities to absolute velocities for use in the conservation of linear momentum equation.

Chapter 6 — Conservation of Angular Momentum

1. Define, explain, compare and contrast the following terms and concepts:
   • Motion of a rigid body
     • Rectilinear translation vs. curvilinear translation
     • Rotation about a fixed axis
     • General motion
   • Rotational motion
   • Angular position: \(\theta\) \([\mathrm{radians}]\)
     • Angular velocity: \(\omega\) \([\mathrm{radians} / \mathrm{second}]\)
     • Angular acceleration: \(\alpha\) \([\mathrm{radians} / \mathrm{seconds}^{2}]\)
       
   • Angular momentum about origin \(O\)
     • angular momentum about the origin \(O\) for a particle: \(\quad \mathbf{L}_{O}=\mathbf{r} \times m \mathbf{V}\)
     • specific angular momentum about the origin \(O\): \(\quad \mathbf{l}_{O}=\mathbf{r} \times \mathbf{V}\) where \(\mathbf{r}\) is the position vector with respect to the origin \(O\)
       • right-hand rule sign convention
       • vector nature of angular momentum
       • units of angular momentum \((\mathrm{N} \cdot \mathrm{m} \cdot \mathrm{s}; \mathrm{~lbf} \cdot \mathrm{ft} \cdot \mathrm{s})\)
         
   • Application of Accounting Principle for Angular Momentum
     • rate of accumulation of angular momentum with the system
       • amount of angular momentum about origin \(O\): \(\quad \displaystyle \mathbf{L}_{O, \ sys} = \int\limits_{ V\kern-0.5em\raise0.3ex- _{sys}} (\mathbf{r} \times \mathbf{V}) \rho \ d V\kern-0.8em\raise0.3ex- \)
       • mass moment of inertia about a single axis: \(\quad \displaystyle I_{G} = \int\limits_{V\kern-0.5em\raise0.3ex- _{sys}} r^{2} \rho \ dV\kern-0.8em\raise0.3ex-\)
       • relation between mass moment of inertia, angular momentum, and angular velocity
     • transport rate of angular momentum across system boundaries
       • transport with forces
         • torques or moments of an external force about origin \(O: \quad \displaystyle \sum \mathbf{r} \times \mathbf{F}_{\text {ext}}\)
         • torque or moment of a couple: \(\quad \mathbf{M}_{O}\)
     • mass transport of angular momentum about the \(O: \quad \displaystyle \sum \dot{m}(\mathbf{r} \times \mathbf{V})_{\text {in}} - \sum \dot{m}(\mathbf{r} \times \mathbf{V})_{\text{out}}\)
     • generation/consumption of angular momentum within the system
       • Empirical Result ----- Angular momentum is conserved!
   • Conservation of Angular Momentum (about the origin \(O\))
     • rate form: \(\quad \displaystyle \frac{d \mathbf{L}_{O, \ sys}}{dt} = \underbrace{\sum \mathbf{M}_{O, \text { external}}}_{\text {Due to couples}} + \underbrace{\sum\left(\mathbf{r} \times \mathbf{F}_{\text {external}}\right)}_{\text {Due to forces}} + \underbrace{\sum_{\text {in}} \dot{m}_{i}(\mathbf{r} \times \mathbf{V})_{i} - \sum_{\text {out}} \dot{m}_{e}(\mathbf{r} \times \mathbf{V})_{e}}_{\text {Due to mass transport}}\)
   • Angular Impulse
     
   • SPECIAL CASE: Plane, Translational Motion of a Closed, Rigid System
     • angular momentum about origin \(O: \quad \mathrm{L}_{O, \ sys} = \mathbf{r}_{G} \times \mathrm{m} \mathbf{V}_{G}\) \[\text{where} \begin{array}{ll} & \mathbf{r}_{G} &= \text{the position vector of the center of mass with respect to the origin.} \\ & \mathbf{V}_{G} &= \text{the velocity of the center of mass.} \end{array} \nonumber \]
     • Conservation of Angular Momentum: \[\begin{aligned} \frac{d \mathbf{L}_{O, \ sys}}{dt} &= \sum \mathbf{r} \times \mathbf{F}_{\text{ext}} + \sum \mathbf{M}_{O} \\ \frac{d}{dt} \left(\mathbf{r}_{G} \times m \mathbf{V}_{G}\right) &= \sum \mathbf{r} \times \mathbf{F}_{\text{ext}} + \sum \mathbf{M}_{O} \\ \underbrace{\cancel{\left[\frac{d \mathbf{r}_{G}}{dt} \times m \mathbf{V}_{G} \right]}}_{\text{since } \mathbf{V}_{G} \times \mathbf{V}_{G} = 0} + \left[\mathbf{r}_{G} \times m \frac{d \mathbf{V}_{G}}{dt} \right] &= \sum \mathbf{r} \times \mathbf{F}_{\text{ext}} + \sum \mathbf{M}_{O} \\ \mathbf{r}_{G} \times m \frac{d \mathbf{V}_{G}}{dt} &= \sum \mathbf{r} \times \mathbf{F}_{\text{ext}} + \sum \mathbf{M}_{O} \end{aligned} \nonumber \] \[\text{where} \begin{array}{ll} & \mathbf{r} &= \text{the position vector with respect to the origin.} \\ & \mathbf{r}_{G} &= \text{the position vector of the center of mass with respect to the origin.} \end{array} \nonumber \]
2. Apply conservation of angular momentum to solve problems involving
   1. steady-state open or closed systems,
   2. static (stationary) closed systems,
   3. closed, stationary, rigid-body systems,
   4. translating, closed, rigid body systems, i.e. systems with \(\omega=0\) and \(\alpha=0\). (See item number 2 from the objectives for linear momentum to see necessary steps.)

Chapter 7 — Conservation of Energy

1. Define, illustrate, and compare and contrast the following terms and concepts:
   • Work-Energy Principle
     • relation to conservation of linear momentum
       
   • Energy
     • internal energy
       • specific internal energy: \(\quad u\)
     • mechanical energy
     • gravitational potential energy
       • specific gravitational potential energy: \(\quad g_{z}\)
     • kinetic energy
       • specific kinetic energy: \(\quad V^{2}/2\)
     • spring energy
       
   • Work
     • mechanism for transferring energy
     • mechanical work vs. thermodynamic work
     • work \((W)\) vs. power \((\dot{W})\)
     • path function
     • reversible (quasiequilibrium) work vs. irreversible work types
       • compression/expansion \((\mathrm{pdV})\) work
       • shaft work
       • elastic (spring) work
       • electric work/power
         • dc power
         • ac power:
           • effective vs maximum values
           • power factor
             
   • Heat transfer
     • mechanism for transferring energy
     • heat transfer \((Q)\) vs. heat transfer rate \((\dot{Q})\)
     • adiabatic surface or boundary
     • path function
     • types of heat transfer
       • conduction
       • convection
         • Newton’s law of cooling
         • convection heat transfer coefficient
       • thermal radiation
         
   • Application of Accounting Principle to Energy
     • rate of accumulation of energy within the system
       • amount of energy \quad \(\displaystyle E_{sys} = \int\limits_{V} e \rho \ dV\) where the specific energy is defined as \(e=u+\left(V^{2}\right) / 2+g z\)
     • transport rate of energy by heat transfer: \(\quad Q\) ----- Heat transfer rate
     • transport rate of energy by work at non-flow boundaries: \(\quad \dot{W}\) ----- Power
     • transport rate of energy by work at flow boundaries: \(\quad \displaystyle \boxed{\sum \left(pv\right) \dot{m}_{\text{in}} - \sum \left(pv\right) \dot{m}_{\text{out}} }\) ----- Flow Power
     • transport rate of energy mass flow: \(\quad \displaystyle \boxed{\sum \dot{m} \left(u+\frac{V^{2}}{2}+gz\right)_{\text {in}} - \sum \dot{m} \left(u+\frac{V^{2}}{2}+gz\right)_{\text {out}} }\)
       
   • Rate form of Conservation of Energy \[\frac{d E_{sys}}{dt} = \dot{Q}_{\text {Net, in}} + \dot{W}_{\text {Net, in}} + \sum \left(h+\frac{V^{2}}{2}+g z\right) \dot{m}_{\text {in}} - \sum\left(h+\frac{V^{2}}{2}+g z\right) \dot{\mathrm{m}}_{\text {out}} \nonumber \] \[\text{where } h = u + pv \text{ is a new property called enthalpy} \nonumber \]
     
   • Substance models
     • Ideal gas with room-temperature specific heats
     • Incompressible substance with room-temperature specific heats
       
   • Thermodynamic cycles
     • Definition (three parts)
     • Classifications
       • Working fluid: single vs two-phase
       • Structure: Closed, periodic vs Closed-loop, steady-state
       • Purpose: Power vs Refrigeration vs Heat Pump cycles
     • Measures of Performance
       • General definition
         • Power cycles \(\rightarrow\) Thermal efficiency \(\quad \eta\)
         • Refrigeration cycle \(\rightarrow\) Coefficient of Performance \(\quad \mathrm{COP}_{\text{ref}}\)
         • Heat pump cycles \(\rightarrow\) Coefficient of Performance \(\quad \mathrm{COP}_{\mathrm{hp}}\)
           
2. Given a mechanical system consisting of particles, apply the Work-Energy Principle where appropriate to solve problems where changes in mechanical energy (kinetic, potential, and spring) can be balanced with mechanical work done on the system.
3. Given a closed or open system and sufficient information about the properties of the system, apply conservation of energy to determine changes in energy (rates of change) within the system and heat transfers (heat transfer rates) and work transfers of energy (power) with the surroundings.
4. Given sufficient information, determine the change in specific internal energy \(\Delta u\) and the change in \(\Delta h\) for a substance that can be modeled using one of the following substance models:
   \(\quad\) Ideal gas with room-temperature specific heats
   \(\quad\) Incompressible substance with room-temperature specific heats
   and use this information in conjunction to meet Objective 3 above.
5. Given the indicated information, calculate the magnitude and the direction of the associated work transfer of energy or power for the system:
   • Given a relation between system pressure and system volume, calculate the compression/expansion work for the system.
   • Given a torque and a rotational speed for a shaft, calculate the shaft power transmitted by the shaft.
   • Given an electric current and the corresponding voltage difference across the terminals, calculate the electric power supplied to or by the system. (You should be able to perform this calculation for both DC and AC systems.)
6. Given a numerical value for a typical energy or power quantity, make the appropriate unit conversions to change the units to the requested values, e.g. convert \(\mathrm{ft}^{2} / \mathrm{s}^{2}\) to \(\mathrm{Btu} / \mathrm{lbm}\).
7. Given a device that operates in a closed-periodic cycle or a closed-loop, steady-state cycle,
   • determine whether the device operates as a power cycle (heat engine) or a refrigerator or heat pump, and
   • calculate the appropriate measure of performance for the specific device, i.e. a thermal efficiency for a power cycle and a coefficient of performance (COP) for a refrigerator or heat pump.
8. List the appropriate assumptions to recover the mechanical energy balance from the general conservation of energy equation.

Chapter 8 — Entropy Production and Accounting

1. Define, illustrate, and explain the following terms and concepts:
   • Second Law of Thermodynamics
   • Reversible processes
     • internally reversible vs internally irreversible
   • Entropy
     • units: \(\mathrm{kJ} / \mathrm{K} ; \mathrm{~Btu} /{ }^{\circ} \mathrm{R}\)
     • specific entropy: \(s\)
       • units: \(\mathrm{kJ} /(\mathrm{K} \cdot \mathrm{kg}) ; \mathrm{~Btu} /\left({ }^{\mathrm{R}} \cdot \mathrm{lbm}\right)\)
   • Thermodynamic temperature
     
   • Application of Accounting Principle for Entropy
     • rate of accumulation of entropy within the system
       • amount of entropy within the system: \(\quad \displaystyle \boxed{S_{sys} = \int\limits_{V} s \rho \ dV}\)
     • transport rate of entropy across system boundaries
       • transport rate of entropy by heat transfer: \(\quad \displaystyle \sum \frac{\dot{Q}_{j}}{T_{b, \ j}}\)
       • transport rate of entropy by mass flow: \(\quad \displaystyle \sum_{\text{in}} \dot{m}_{i} s_{i} - \sum_{\text{out}} \dot{m}_{e} s_{e}\)
     • production/consumption of entropy
       • EMPIRICAL EVIDENCE ----- Entropy can only be produced and in the limit of an internally reversible process entropy is conserved.
       • Rate of entropy production: \[\dot{S}_{\text {gen }} \left\{ \begin{array}{l} >0 \text { Internally irreversible } \\ =0 \text { Internally reversible } \end{array}\right. \nonumber \]
         
   • Accounting Equation for Entropy
     • rate form: \(\quad \displaystyle \boxed{\frac{d S_{sys}}{dt} = \sum \frac{\dot{Q}_{j}}{T_{b, \ j}} + \sum_{\text{in}} \dot{m}_{i} s_{i} - \sum_{\text{out}} \dot{m}_{e} s_{e} + \dot{S}_{\text{gen}} }\)
   • Carnot Efficiency for a Power Cycle
   • Isentropic Process
     
2. Apply the accounting equation for entropy in conjunction with the conservation of energy equation to calculate the entropy generation rate or entropy generation for a steady-state device or cycle.
3. Given sufficient information, determine the specific entropy change \(\Delta s\) for a substance when one of the following models apply:
   • Ideal gas with room-temperature specific heats
   • Incompressible substance with room-temperature specific heats
4. Apply the entropy accounting equation in conjunction with the conservation of energy equation to calculate the entropy generation or the entropy generation rate for a system when all other necessary information is known.
5. Apply the accounting equation for entropy in conjunction with the conservation of energy equation to determine the theoretical "best" performance, i.e. theoretical maximum thermal efficiency or coefficient of performance for a cycle.
6. Determine if a specific device or system is operating in a reversible fashion, an irreversible fashion, or is not physically possible.
7. Evaluate the performance of a device or system when it is operating in an internally reversible fashion.