EGR 2500 Thermodynamics: Chapter 6 and 7
Heat Pump
A device that transfers heat from a low temperature medium to a high temperature one
What is the energy balance equation for a uniform flow system?
(Qin + Win + ΣmΘin) - (Qout + Wout + ΣmΘout) = (m2e2 - m1e1)system where Θ = h +ke + pe is the energy of a fluid stream at any inlet or exit per unit mass and e = u + ke + pe is the energy of the non-flowing fluid within the control volume per unit mass
How can the conservation of mass principle for a control volume be expressed in word and variable form?
(Total mass entering the CV during ▲t) - (Total mass leaving the CV during ▲t) = (Net change of mass within CV during ▲t) OR min - mout = ▲mcv , where ▲mcv = mfinal - minitial is the change in the mass of the control volume during the process
How do you represent the work done in pushing the fluid element across the boundary (i.e. flow work)?
*Force must act through distance L to push entire fluid element into control volume Wflow = FL = PAL = PV (kJ)
What is the relationship between temperature and quality?
*More of the higher temp thermal energy can be converted to work -The higher the temperature, the higher the quality of energy
What are geothermal heat pumps? What is the COP of these heat pumps?
- AKA ground source heat pumps - Heat pumps that use the ground as a heat source - Require the burial of pipes in the ground 1-2 m deep - More expensive but more efficient (45% more efficient than air source heat pumps) - COP is as high as 6
How do you analyze the PV diagram of the Carnot cycle?
- Area under process curve represents boundary work for quasi equilibrium (internally reversible) processes - Area under curve 1-2-3 is work done by gas during expansion part of cycle - Area under curve 3-4-1 is the work done on the gas during the compression part of the cycle -Area enclosed by path of cycle represents the net work done during the cycle.
Why are heat engines built? Why are engineers constantly trying to improve the efficiencies of these devices?
- Built for the purpose of converting heat to work - Constantly trying to improve the efficiencies of these devices since increased efficiency means less fuel consumption and thus lower fuel bills and less pollution,
What can be said about reversible cycles?
- Cannot be achieved in practice because the irreversibilities associated with each process cannot be eliminated. - Provide upper limits on performance of real cycles - Serve as starting points in development of actual cycles and are modified as needed to meet certain requirements
Give some examples of unsteady flow processes.
- Charging of rigid vessels from supply lines - Discharging a fluid from a pressurized vessel - Driving a gas turbine with pressurized air stored in a large container - Inflating tires or balloons - Cooking with an ordinary pressure cooker
What does the Clausius statement imply?
- DOES NOT imply that a cyclic device that transfers heat from a cold medium to a warmer one is impossible to construct (this is what a household refrigerator does) - Simply states that a refrigerator cannot operate unless its compressor is driven by an external power source, such as an electric motor
What is the relationship between TH, TL, and efficiency of a Carnot heat engine? Why?
- Efficiency of a Carnot heat engine increases as TH is increased or as TL is decreased *This is expected because as TL decreases, so does the amount of heat rejected and as TL approaches 0., the Carnot efficiency approaches unity
What part of a household refrigerator serves as the evaporator? Which parts serves as the condenser?
- Evaporator - freezer compartment where heat is absorbed by refrigerant - Condenser - Coils behind the fridge where heat is dissipated to kitchen air
What are irreversibilities? Give some examples.
- Factors that cause a process to be irreversible, such as friction, unrestrained expansion, mixing of 2 fluids, heat transfer across a finite temperature difference, electric resistance, inelastic deformation of solids, and chemical reactions.
What are air source heat pumps? What is the COP of such heat pumps? Why are they not appropriate for cold climates?
- Heat pumps that use the cold outside air as the heat source in winter - COP is about 3.0 - Not appropriate for cold climates since their efficiency drops considerably when temperatures are below freezing point
Why is work a more valuable form of energy in comparison to solar ponds AKA heat?
- More valuable because 100% of work can be converted to heat, but only a fraction of heat can be converted to work - When heat is transferred from high temp body to lower temp one, it is degraded since less of it now can be converted to work
What is an alternate way to express the Kelvin-Planck statement?
- No heat engine can have a thermal efficiency of 100% or - For a power plant to operate, the working fluid must exchange heat with the environment as well as the furnace
What is the limitation of the first law of thermodynamics?
- Processes proceed in a certain direction and not in the reverse direction - First law places no restriction on direction of a process, but satisfying the first law does not ensure that process can actually occur
What are the quantities associated with a refrigeration system?
- QL = magnitude of heat removed from refrigerated space at temperature TL - QH = magnitude of heat rejected to warm environment at temperature TH - Wnet, in = net work input to refrigerator
How are COPR and COPHP related? What does this relation imply?
COPHP = COPR + 1 - This relation implies that the coefficient of performance of a heat pump is always greater than unity since COPR is a positive quantity.
Compare and contrast reversible and irreversible processes in terms of how restoration to the initial state is made.
- Reversible processes - restoration is made without leaving any net change on the surroundings - Irreversible processes - surroundings usually do some work on the system and therefore does not return to their original state
What are solar ponds? What is their use? What are the disadvantages of using them?
- Solar ponds - large bodies of water where large quantities of solar energy can be stored - Stored energy can be supplied to a heat engine to produce work (electricity) - Efficiency is very low (<5%) because of low quality of energy stored in the source - Construction and maintenance costs are high - Temp and quality of solar energy stored could be raised by utilizing concentrating collectors`
What is significant about the 4 components of the steam power plant?
- The 4 components involve mass flow in and out, and therefore should be treated as open systems. - Components and connecting pipes always contain the same fluid - No mass enters or leaves
What is second law efficiency? What does this enable?
- The degree of approximation to corresponding reversible processes - Enables us to compare the performance of different devices that are designed to do the same task on the basis of their efficiencies
What are the requirements in order for a body to be considered/modeled as a thermal energy reservoir?
A body does not actually have to be very large to be considered a reservoir. Any physical body whose thermal energy capacity is large relative to the amount of energy it supplies or absorbs can be modeled as one.
What conclusions can be made about an unsteady flow system given that the state of an unsteady flow system may change with time?
- The state of mass leaving the control volume at any instant is the same as the state of the mass in the control volume at any instant - Initial and final properties of control volume can be determined from knowledge of initial and final states
How do the thermal efficiencies of actual and reversible heat engines operating between the same temp limits compare?
- Thermal efficiency < Thermal Efficiency Rev --> irreversible heat engine - Thermal efficiency = Thermal Efficiency Rev --> reversible heat engine - Thermal efficiency > Thermal Efficiency --> impossible heat engine
What is significant to understand about reversible processes?
- They actually do not occur in nature. - They are merely idealizations of actual processes - Can be approximated by actual devices, but never achieved.
What are the characteristics that define a heat engine?
- They receive heat from a high temp source (solar energy, oil furnace, nuclear reactor, etc) - They convert part of this heat to work (in the form of a rotating shaft) - They reject remaining waste heat to a low temp sink (atmosphere, rivers, etc) - They operate on a cycle
What are the characteristics that set unsteady flow processes apart from steady flow processes?
- Unsteady flow processes start and end over some finite time period instead of continuing indefinitely. - Deal with changes that happen over some time interval ▲t instead of with the rate of changes. - Mass within the system boundaries does not remain constant during a process - Usually stationary - fixed in space, but may involve moving boundaries and thus work
What are some other applications of the second law of thermodynamics?
- Used to determine the theoretical limits for performance of commonly used engineering systems and predicting the degree of completion of chemical reactions - Defines perfection for thermodynamic processes - quantifies level of perfection and points the direction to eliminate imperfections efficiently
How is best performance achieved? Why is this the case?
- Using units equipped with variable speed drives (inverters) - They allow the unit to operate at maximum efficiency for varying heating/cooling needs and weather conditions as determined by a microprocessor
Why is friction considered to be an inrreversiblity?
- When motion of moving bodies is reversed, bodies are restored to original positions, but the interface doesn't cool and heat is not converted back to work. - More of the work is converted to heat while overcoming the friction forces that oppose the reverse motion. - Process is irreversible since moving bodies and surroundings cannot be returned to their original states
Why is unrestrained expansion of a gas separated from a vacuum by a membrane considered to be an irreversibility?
- When the membrane is ruptured, gas fills entire tank - Only way to restore system to original state is to compress it to its initial volume, while transferring heat from the gas until it reaches initial temp - Amount of heat transferred from the gas equals amount of work done on gas by the surroundings - Restoration of surroundings involves conversion of this heat completely to work, which violates the second law
What is the relationship between Celsius and Kelvin temperatures?
-Magnitudes of temp units on Kelvin and Celsius scales are identical and differ by a constant 273.15 T(C) = T(K) - 273.15
What observations can be made about a steady flow process?
-No intensive or extensive properties within the control volume change with time -Volume, mass, and total energy content of control volume all remain constant -Boundary work is 0 -Total mass or energy entering control volume must be equal to total mass or energy leaving it
How are QH and QL defined in order to bring uniformity to the treatment of heat engines, refrigerators, and heat pumps?
-QH = magnitude of heat transfer between the cyclic device and the high temperature medium at temperature TH -QL = magnitude of heat transfer between the cyclic device and the low temperature medium at temperature TL
How do refrigerators and heat pumps differ in their objectives?
-Refrigerator - maintain the refrigerated space at a low temperature by removing heat from it. *Discharging the heat to a higher temperature medium is a necessary part of the operation, not the purpose - Heat pump - maintain a heated space at a high temperature which is accomplished by absorbing heat from a low temperature source and supplying this heat to the high temperature medium
Describe the steps of the vapor compression refrigeration cycle.
1. Refrigerant enters compressor as a vapor and is compressed to condenser pressure. 2. Leaves compressor at relatively high temp, cools down, and condenses as it flows through coils of condenser by rejecting heat to surrounding medium. 3. Enters capillary tube where its pressure and temp drop drastically because of throttling effect. 4. Low temp refrigerant enters evaporator where it evaporates by absorbing heat from refrigerated space. 5. Cycle completed as refrigerant leaves evaporator and reenters the compressor
What are the 2 Carnot Principles?
1. The efficiency of an irreversible heat engine is always less than the efficiency of a reversible one operating between the same 2 reservoirs. 2. The efficiencies of all reversible heat engines operating between the same 2 reservoirs are the same
When the performance of actual heat engines is assessed, the efficiencies should not be compared to ____________________, but rather they should be compared to _____________
100% ; efficiency of a reversible heat engine operating between same temp limits because this is the true theoretical upper limit for the efficiency
Most air conditioners or heat pumps in the market have SEER values from ___________ to _______________, which correspond to COP values of _____________ to __________________.
13 ; 21 ; 3.8 ; 6.2
What are the 3 parts that the total energy of a simple compressible system is comprised of? How is the total energy expressed on a unit mass basis?
3 parts - internal, kinetic, and potential energies e = u + ke + pe = u + (V^2 / 2) + gz (kJ/kg) *V is the velocity and z is the elevation of the system relative to some external reference point
What is the maximum efficiency of a steam power plant operating between 300 K and 1000 K?
70%
What is thermal efficiency a measure of?
A measure of how efficiently a heat engine converts the heat that it receives to work
What is the energy efficiency ratio?
A measure of the instantaneous energy efficiency and is defined as the ratio of the rate of heat removal from the cooled space by the cooling equipment to the rate of electricity consumption in steady operation
What is the difference between a nozzle and a diffuser?
A nozzle is a device that increases the velocity of a fluid at the expense of pressure. A diffuser is a device hat increases the pressure of the fluid by slowing it down
What constitutes whether a process can occur or not?
A process cannot occur unless it satisfies both the first and second law of thermodynamics
What is the steady flow process?
A process during which a fluid flows through a control volume steadily, i.e. the fluid properties can change from point to point within the control volume, but at any point, they remain constant during the entire process
Refrigerators
A special device that transfers heat from a low temperature medium to a high temperature one
What happens during an internally reversible process? What does this indicate?
A system proceeds through a series of equilibrium states, and when the process is reversed, the system passes through exactly the same equilibrium states when returning to initial state *Paths of the forward and reverse processes coincide for an internally reversible process
What is the Kelvin scale?
A temperature scale based on absolute temperatures where the temperature ratios depend on the ratios of heat transfer between a reversible heat engine and the reservoirs and are independent of the physical properties of any substance. Temps vary between 0 and infinity
Thermodynamic Temperature Scale
A temperature scale that is independent of the properties of the substances that are used to measure temp
How do the coefficients of performance of actual and reversible refrigerators operating between the same temp limits compare?
COPR < COPR, rev --> irreversible refrigerator COPR = COPR, rev --> reversible refrigerator COPR > COPR, rev --> impossible refrigerator
Describe the efficiency of irreversible heat engines
All irreversible heat engines operating between TH and TL have lower efficiencies
Mass flow rate
Amount of mass flowing through a cross section per unit time
What are throttling valves?
Any kind of flow restricting devices that cause a significant pressure drop in the fluid
How can the COPR relation for refrigeration be expressed knowing that Wnet,in = QH - QL?
COPR = (QL / Wnet,in) = (QL / (QH - QL)) = 1 / ((QH/QL) - 1)
What must be done when performing a general analytic study or solving a problem that involves an unknown work or heat interaction?
Assume a direction for the hear or work interaction
Describe the reversible adiabatic expansion phase in the Carnot cycle.
At state 2, reservoir that was in contact with the cylinder head is removed and replaced by insulation so that system becomes adiabatic. The gas continues to expand slowly, doing work on the surroundings until its temperature drops from TH to TL (state 3). The piston is assumed to be frictionless and the process to be quasi-equilibrium, so the process is reversible and adiabatic.
Describe the reversible isothermal compression phase in the Carnot cycle.
At state 3, the insulation at the cylinder head is removed and the cylinder is brought into contact with a sink at temp TL. Now the piston is pushed inward by an external force doing work on the gas. As the gas is compressed, its temp tends to rise. As soon as it rises by an small amount dT, heat is transferred from the gas to the sink, causing the gas temp to drop to TL. Thus, gas temp remains constant at TL. This is a reversible heat transfer process because temperature diff between the gas and the sink never exceeds dT. Continues until piston reaches state 4. Amount of heat rejected from gas during this process is QL
What is average velocity and how do you calculate it?
Average value of flow velocity Vn across the entire cross section of the pipe Vavg = (1/Ac) ∫VndAc Ac = area of cross section normal to flow direction
What are air conditioners?
Basically refrigerators whose refrigerated space is a room or a building instead of the food compartment
Why is the thermal efficiency of a heat engine always less than unity?
Because both QL and QH are defined as positive quantities
Why does the amount of energy entering a control volume in all forms (by heat, work, and mass) have to be equal to the amount of energy leaving it?
Because during a steady flow process, the total energy content of a control volume remains constant and thus the change in the total energy of the control volume is 0.
Why do the volume flow rates remain nearly constant for the steady flow of fluids?
Because liquids are essentially incompressible substances (constant-density)
Why is a throttling valve called an isenthalpic device?
Because the enthalpy values at the inlet and exit of a throttling valve are the same
Why is it more practical to express mass flow rate in terms of average values over a cross section of the pipe?
Because the integral equation is not very practical or easy to solve
In general, why is it not easy to determine the total energy transported by mass into or out of the control volume? What must be done instead?
Because the properties of the mass at each inlet or exit may be changing with time as well as over the cross section. Only way to determine energy transport through opening as result of mass flow is to consider sufficiently small differential masses dm that have uniform properties and to add their total energies during flow.
How can net work and cycle efficiency be maximized?
By using processes that require the least amount of work and deliver the most by using reversible processes
How is the coefficient of performance for a Heat Pump expressed?
COPHP = (Desired output / Required output) = (QH / Wnet,in)
How can the COPHP relation for heat pumps be expressed knowing that Wnet,in = QH - QL?
COPHP = (QH / WNet,in) = (QH / (QH - QL)) = 1 / (1 - (QL/QH))
Carnot Heat Engine
Hypothetical heat engine that operates on the reversible Carnot cycle
How is the coefficient of performance of any refrigerator or heat pump, reversible or irreversible, expressed?
COPR = 1 / ( (QH/QL) - 1) and COPHP = 1 / (1 - (QL/QH)) *QL = amount of heat absorbed from low temp medium *QH = amount of heat rejected to high temp medium
How can the COP (coefficient of performance) of a refrigerator be expressed?
COPR = desired output / required input = QL = Wnet,in
What are the COP relations for reversible refrigerators and heat pumps?
COPR,rev = 1 / ((TH/TL) - 1) or COPHP, rev = 1 / (1 - (TL/TH))
What task does a pump perform?
Capable of compressing fluids to very high pressures
What task does a compressor perform?
Capable of compressing the gas to very high pressures
What does the term ▲ke = ((V2^2 - V1^2) / 2) stand for in the energy balance equation for a steady flow system? When can this term be neglected?
Change in kinetic energy of the system Kinetic energy term at low velocities can be neglected. When a fluid stream enters and leaves a steady flow device at about the same velocity (V1 = V2) change in kinetic energy is close to 0 regardless of velocity.
What does the term ▲pe = g(z2 - z1) stand for in the energy balance equation for a steady flow system? When can this term be neglected?
Change in potential energy of the system. A potential energy change of 1 kJ/kg corresponds to an elevation difference of 102 m and since the elevation difference between inlet and exit of most industrial devices is well below this value, potential energy term can be neglected for turbines and compressors.
What are the assumptions usually made when determining a direction for unknown heat or work interactions?
Common practice to: - Assume heat to be transferred into the system (heat input) at a rate of Qdot and -Work produced by the system (work output) at a rate of Wdot
What devices are used to increase the pressure of a fluid? How is work supplied to these devices?
Compressors, pumps, and fans *Work is supplied to these devices from an external source through a rotating shaft
Carnot Principles
Conclusions pertaining to the thermal efficiency of reversible and irreversible heat engines that are derived from the Kelvin-Planck and Clausius statements
Why is heat transfer through a finite temperature difference considered to be an irreversibility?
Consider a can of cold soda in a warm room: - Heat is transferred from warmer room air to cooler soda - Only way to reverse process and restore soda to original temp is to provide refrigeration which requires work input. - At the end of the reverse process, soda is restored to initial state but surroundings are not - Internal energy of surroundings increases by an amount equal to work supplied to refrigerator - Restoration of surroundings to initial state can only be done by converting excess internal energy completely to work
How does a control volume differ from a closed system?
Control volumes involve mass flow across their boundaries and some work is required to push mass into or out of the control volume
What is the magnitude of a kelvin defined as?
Defined as 1/273.16 of the temperature interval between absolute zero and the triple point temp of water (273.16 K).
Reversible Process
Defined as a process that can be reversed without leaving any trace on the surroundings, i.e. both the system and the surroundings are returned to their initial states at the end of the reverse process
Describe density in most practical applications.
Density is essentially uniform over the pipe cross section and can be taken out of the integral.
What is the heat transfer rate associated with heat exchangers dependent on?
Depends on how the control volume is selected.
What does the efficiency of a heat engine cycle depend on?
Depends on how the individual processes that make up the cycle are executed
Heat exchangers
Devices where two moving fluid streams exchange heat without mixing
Why is the volume flow rate at the outlet of an air compressor much less than at the inlet, even though mass flow rate of air through the compressor is constant?
Due to the higher density of air at the compressor exit
What is the relationship between EER (or SEER) and COP?
EER = 3.412COPR
What is the equation that suggests that there is an equivalence between mass and energy?
Einstein's formula E = mc^2, where c is the speed of light in a vacuum, m is mass, and E is energy
How is the total energy of a flowing fluid of mass m represented, provided that properties of mass m are uniform?
Emass = m * energy_flowing_fluid = m(h + (V^2 / 2) + gz)
When a fluid stream with uniform properties is flowing with a mass flow rate, how is the rate of energy flow represented?
Emassdot = mass_flow_rate * energy_flowing_fluid = mass_flow_rate(h + (V^2 / 2) + gz)
What is an externally reversible process?
Externally reversible if no irreversibilities occur outside of the system boundaries during the process.
How do you represent the force applied on the fluid element by the imaginary piston in the control volume?
F = PA , where P is fluid pressure and A is the cross-sectional area of the fluid element
True or False: Most engineering devices involve multiple streams.
False - Most engineering devices such as nozzles, diffusers, turbines, compressors, and pumps involve a single stream, i.e. only one inlet and one outlet.
True or False: The flow work relation differs depending on whether the fluid is pushed into or out of the control volume.
False - The fluid work relation is the same whether the fluid is pushed into or out of the control volume.
True or False: The heat transfer process from a low temperature medium to a high temperature medium occurs automatically.
False - a special device is needed for this process
How does the usage of the conservation of mass principle in closed systems differ from how it is used in control volumes?
For closed systems - conservation of mass principle is implicitly used by requiring the mass of the system to remain constant during a process For control volumes - mass can cross boundaries and so you must keep track of the amount of mass entering and leaving the control volume
How is the thermal efficiency of a heat engine expressed?
For heat engines, the desired output is the net work output and the required input is the amount of heat supplied to the working fluid. Thermal efficiency = Net work output / total heat input OR Thermal efficiency = Wnet,out / Qin OR Thermal efficiency = 1 - (Qout/Qin) (Wnet,out = Qin - Qout)
When does heat transfer become significant for a throttling valve?
For throttling devices with large exposed surface areas, such as capillary tubes
Give some examples of cyclic devices.
Heat engines, refrigerators, and heat pumps
What characterizes an externally reversible process?
Heat transfer between a reservoir and a system is externally reversible if the outer surface of system is at temperature of the reservoir
What quantities are negligible for turbines and compressors? Why?
Heat transfer from turbines is usually negligible (Qdot = 0) since they are typically well-insulated. Heat transfer is also negligible for compressors unless there is intentional cooling. Potential energy changes are negligible for both. Velocities in theses devices, with the exception of turbines and fans, are usually too low to cause any significant change in kinetic energy.
When does heat transfer occur? What does this indicate?
Heat transfer occurs when there is a temperature difference between a system and its surroundings, which indicates that it is physically impossible to have a reversible heat transfer process
When should work interactions be considered in a control volume?
If it involves a heating section (electric wires), a fan, or a pump (shaft)
For a throttling process, what happens if the flow energy increases during the process (P2v2 > P1v1)?
If the flow energy increases during the process, it can do so at the expense of the internal energy. As a result, internal energy decreases, which is usually accompanied by a drop in temperature.
For a throttling process, what happens if the product Pv decreases?
If the product Pv decreases, the internal energy and the temperature of a fluid will increase during a throttling process.
Describe the reversible isothermal expansion phase in the Carnot cycle.
In state 1, the temperature of the gas is TH and the cylinder head is in close contact with a source at temperature TH. Gas is allowed to expand slowly, doing work on surroundings. As the gas expands, temp of gas tends to decrease. As soon as the temp drops, some heat is transferred from reservoir into gas, raising gas temp to TH. Thus, gas temp is kept constant at TH. The temp difference between gas and reservoir never exceeds a differential amount dT which implies that this is a reversible heat transfer process. Continues until piston is in state 2. Amount of total heat transferred to gas during process is QH
How is the efficiency of a refrigerator expressed?
In terms of the coefficient of performance (COPR)
How is the measure of performance of a heat pump expressed?
In terms of the coefficient of performance COPHP
What task does a fan perform?
Increases the pressure of a gas slightly and is mainly used to mobilize gas
What are heat exchangers intended for?
Intended for heat transfer between 2 fluids within the device and the outer shell is well insulated to prevent heat loss to surrounding medium
What is an internally reversible process?
Internally reversible if no irreversibilities occur within boundaries of system during process
What is friction?
Irreversibility associated with bodies in motion. *When 2 bodies in contact are forced to move relative to each other, a friction force that opposes the motion develops at the interface of these 2 bodies, and some work is needed to overcome this friction force. *Energy supplied as work is eventually converted to heat during the process and is transferred to bodies in contact. * Temperature rise at interface
Why can a two-phase system be modeled as a thermal energy reservoir?
It can absorb and release large quantities of heat while remaining at constant temperature
What is convenient to have in developing the second law of thermodynamics?
It is convenient to have a hypothetical body with a relatively large thermal energy capacity (mass X specific heat) that can supply or absorb finite amounts of heat without undergoing any change in temp *Called a thermal energy reservoir
Why is it difficult to analyze the general unsteady flow process?
It is difficult to analyze because the properties of the mass at the inlets and exits may change during a process
What is important to do when analyzing unsteady flow processes?
It is important to keep track of the mass and energy contents of the control volume as well as the energy interactions across the boundary.
What does the Kelvin-Planck statement state?
It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.
Why can an actual heat engine (i.e. irreversible) not reach the maximum theoretical efficiency?
It is impossible to completely eliminate all the irreversibilities associated with the actual cycle.
What does the Clausius statement state?
It is impossible to construct a device that operates in a cycle and produces no effect other than transfer of heat from lower temperature body to a higher temperature body.
What is the conservation of energy equation for a throttling valve?
It is reduced to h1 = h2 which means that enthalpy values at the inlet and exit of a throttling valve are the same.
How is the term heat engine used in a broader sense? Why do these devices operate in a mechanical cycle but not in a thermodynamic cycle?
It is used to include work producing devices that don't operate in the thermodynamic cycle, such as engines that involve internal combustion (gas turbines and car engines). *Operate in mechanical cycle but not a thermodynamic cycle since the working fluid (combustion gases) does not undergo a complete cycle.
What is the difference between the Kelvin-Planck Statement and the Clausius statement?
Kelvin-Planck - related to heat engines Clausius - Related to refrigerators or heat pumps
What things can accurately be modeled as thermal energy reservoirs? Why?
Large bodies of water such as oceans, lakes, and rivers, as well as the atmospheric air can be modeled as thermal energy reservoirs *Because of their large thermal energy storage capabilities or thermal masses
What is the simple rule to follow when selecting a control volume?
Make the control surface normal to the flow at all locations where it crosses the fluid flow. This way the dot product of V and n simply becomes the magnitude of velocity and the integral ∫ρ(V*n)dA becomes ρVA
When is the amount of heat gained or lost by the fluid significant?
May be significant if the pipe or duct is long.
What quantities are usually negligible for a mixing chamber? What quantities are left?
Mixing chambers are usually well insulated (q = 0) and do not involve any kind of work (w = 0). Kinetic and potential energies of the fluid streams are usually negligible. *all that is left in the energy equation is total energies of incoming streams and outgoing mixture
What does steady mean?
No change with time
What are you interested in when dealing with steady flow processes?
Not interested in the amount of mass that flows in or out of a device over time Instead interested in amount of mass flowing per unit time, i.e. the mass flow rate
Why must the kinetic energy changes be accounted for when analyzing the flow through nozzles and diffusers?
Nozzles and diffusers involve very high velocities and as a fluid passes through a nozzle or diffuser, it experiences large changes in its velocity.
How is the mass flow rate through the entire cross-sectional area of a pipe or duct obtained? What is the equation?
Obtained through integration mass flow rate = ∫δm = ∫ρVndAc
Give some examples of throttling valves.
Ordinary adjustable valves, capillary tubes, and porous plugs.
What happens if heat transfer is undesirable?
Pipes or ducts are insulated to prevent any heat loss or gain, particularly when temp difference between flowing fluid and surroundings is large
When is a reversible process possible?
Possible only if the net heat and net work exchange between the system and the surroundings is 0 for the original and reverse processes.
What happens as a result of the heat or work interactions between a steady flow system and its surroundings not changing with time?
Power delivered by the system and the rate of heat transfer to or from a system remain constant during steady flow process.
Unsteady flow / transient flow processes
Processes that involve changes within the control volume with time
Irreversible Processes
Processes that occur in a certain direction. Once having taken place, these processes cannot reverse themselves spontaneously and restore the system to its initial state. EX) Once a cup of coffee cools, it will not heat up by retrieving the heat it lost from the surroundings.
What is the steady flow energy balance equation for single stream devices?
Qdot - Wdot = mass_flow_rate * (h2 - h1 + ( (V2^2 - V1^2) / 2) + g(z2 - z1) *to obtain the equation on a unit mass basis, divide both sides by mass_flow_rate
How can the energy balance for a general steady flow system be written?
Qdotin + Wdotin + Σmass flow rate * energy_flowing_fluid (in) = Qdotout + Wdotout + Σmass flow rate * energy_flowing_fluid (out) where energy_flowing_fluid = h + (V^2/2) + gz
What are the quantities involved with a basic steam power plant? What do they signify?
Qin = amount of heat supplied to steam in boiler from a high temperature source (furnace) Qout = amount of heat rejected from steam in condenser to a low temperature sink (atmosphere, river, etc) Wout = amount of work delivered by steam as it expands in turbine Win = amount of work required to compress water to boiler pressure
What is rate of heat transfer associated with nozzles and diffusers?
Rate of heat transfer between fluid flowing through a nozzle or diffuser and the surroundings is pretty small (close to ) since the fluid has high velocities and doesn't spend enough time in device for a significant heat transfer to take place.
What does the term Qdot stand for in the energy balance equation for a steady flow system? What are the sign conventions for this term?
Rate of heat transfer between the control volume and its surroundings Qdot is negative --> when the control volume is losing heat Qdot is 0 --> control volume is well insulated (adiabatic)
What does the conservation of mass principle for a heat exchanger in steady operation require?
Requires that the sum of inbound mass flow rates equal sum of outbound mass flow rates *Under steady operation, the mass flow rate of each fluid stream flowing through a heat exchanger remains constant
What does the conservation of mass principle for a mixing chamber require?
Requires that the sum of the incoming mass flow rates equal the mass flow rate of the outgoing mixture.
Describe the differences between what is described in the first law of thermodynamics compared to what is described in the second law of thermodynamics.
Second law of thermodynamics identifies the direction of processes, as well as asserts that energy has quality in addition to quantity. -The first law is concerned with quantity of energy and transformations of that energy from one form to another with no regard to its quality. - Second law provides the means to determine the quality as well as the degree of degradation of energy during a process
Mixing chamber
Section where the mixing process takes place
What is the simplest form of a heat exchanger? How does it work?
Simplest form - double tube heat exchanger. -Composed of 2 concentric pipes of different diameters - One fluid flows in inner pipe and the other in the space between the 2 pipes - Heat is transferred from hot fluid to cold fluid through wall separating them - Inner tube sometimes makes turns inside shell to increase heat transfer area and rate of heat transfer
Why is it significant that energy reservoirs are characterized by their temps?
Since energy reservoirs are characterized by their temps, the thermal efficiency of reversible heat engines is a function of reservoir temps only.
What is significant to note about volume flow rates into and out of a steady flow device?
Since there is no such thing as a conservation of volume principle, volume flow rates into and out of a steady flow device may be different, even though mass flow rates are conserved.
What is the difference between a source and a sink?
Source - reservoir that supplies energy in the form of heat Sink - reservoir that absorbs energy in the form of heat
What does the term ▲h = h2 - h1 stand for in the energy balance equation for a steady flow system? Where do these values come from?
Stands for the enthalpy change of a fluid. Values can be determined by reading enthalpy values at the exit and inlet states from the tables. For ideal gases => h = cpavg(T2 - T1)
Describe the reversible adiabatic compression phase in the Carnot cycle.
State 4 is such that when the low temp reservoir is removed, the insulation is put back on the cylinder head, and the gas is compressed in a reversible manner; the gas returns to its initial state (state 1). Temp rises from TL to TH during this reversible adiabatic compression process.
What does the second Carnot principle state and what does this signify?
States that all reversible heat engines have the same thermal efficiency when operating between the same two reservoirs, which means that the efficiency of a reversible engine is independent of the working fluid employed and its properties, the way the cycle is executed, or the type of reversible engine used.
What does the conservation of mass principle for a general steady flow system with multiple inlets and outlets state?
States that the total rate of mass entering a control volume is equal to the total rate of mass leaving it
Give some examples of steady flow devices. Why are they called steady flow devices?
Steady flow devices - turbines, compressors, and nozzles They operate for a long periods of time under the same conditions once the transient start up period is completed and steady operation is established
What is significant to note about the COP of a reversible refrigerator or heat pump?
The COP of a reversible refrigerator or heat pump is max theoretical value for specified temp limits
What is the relationship between COP of refrigerators and heat pumps and TL? What does this signify?
The COPs of both refrigerators and the heat pumps decrease as TL decreases which means that it requires more work to absorb heat from low temp medium. As the temp of refrigerated space approaches 0, amount of work required to produce finite amount of refrigeration approaches infinity and COPR approaches 0.
What is the thermodynamic temperature scale that is used?
The Kelvin scale
What does a negative quantity for Q (heat) or W (work) indicate?
The assumed direction is wrong and should be reversed
What is the Carnot cycle?
The best known reversible cycle that is composed of 4 reversible processes - 2 isothermal and 2 adibatic - and it can be executed either in a closed or a steady flow system
What is the net work output of a power plant?
The difference between the total work output of the plant and the total work input Wnet,out = Wout - Win
What is the idealization associated with the uniform flow process?
The fluid flow at any inlet or exit is uniform and steady, and thus the fluid properties do not change with time or position over the cross section of an inlet or exit. If they do, they are averaged and treated as constants for the entire process.
Working fluid
The fluid to and from which heat is transferred while undergoing a cycle in heat engines and other cyclic devices.
What is thermal efficiency?
The fraction of the heat input that is converted to net work output ; a measure of the performance of a heat engine
What is the Carnot efficiency?
The highest efficiency a heat engine operating between the two thermal energy reservoirs at temps TL and TH can have
What is the relationship between friction and irreversibility?
The larger the friction forces involved, the more irreversible the process is
What forms the basis for the Kelvin-Planck statement?
The limitation on the thermal efficiency of heat engines forms the basis for the Klevin-Planck statement
How can the conservation of mass principle for a control volume be expressed in paragraph form?
The net mass transfer to or from a control volume during a time interval ▲t is equal to the net change (increase or decrease) of the total mass within the control volume during ▲t
Why are throttling devices commonly used in refrigeration and air conditioning applications?
The pressure drop in the fluid is often accompanied by a large drop in the temperature
What is the seasonal energy efficiency ratio?
The ratio of the total amount of heat removed by an air conditioner or heat pump during a normal cooling season to the total amount of electricity consumed *Measure of seasonal performance of cooling equipment
What is the Carnot Refrigeration cycle?
The reverse of the Carnot heat engine cycle -Cycle remains exactly the same except directions of heat and work interactions are reversed. - Heat in the amount QL is absorbed from low temp reservoir - Heat in amount QH is rejected to high temp reservoir - Need a work input of Wnet, in
What occurred as a result of the first law's inability to identify whether a process can take place?
The second law of thermodynamics was introduced
What is a work producing device that best fits into the definition of a heat engine?
The steam power plant which is an external combustion engine - combustion takes place outside the engine and the thermal energy released during this process is transferred to steam as heat.
Why can the industrial furnace be modeled as a thermal energy reservoir?
The temperatures of most furnaces are carefully controlled and they are capable of supplying large quantities of thermal energy as heat in an essentially isothermal manner
How can the thermal efficiency of actual heat engines be maximized?
The thermal efficiency of actual heat engines can be maximized by supplying heat to the engine at the highest possible temperature (limited by material strength) and rejecting heat from the engine at the lowest possible temp (limited by temp of cooling med)
What device drives the electric generator in steam, gas, or hydroelectric power plants? How does this device work?
The turbine *As the fluid passes through the turbine, work is done against the blades, which are attached to the shaft. As a result, the shaft rotates, and the turbine produces work.
What is flow work and why is it necessary?
The work required to push the mass into or out of the control volume. *Necessary for maintaining a continuous flow through a control volume
What terms are negligible for heat exchangers?
There are typically no work interactions (w = 0) and negligible kinetic and potential energy changes for each fluid stream
What is the work associated with throttling valves?
There is no work done (w = 0)
What is the relationship between the Kelvin-Planck statement and the Clausius statement?
They are equivalent in their consequences and either statement can be used as the expression of the second law of thermodynamics *Any device that violates the Kelvin-Planck statement also violates the Clausius statement and vice versa.
Why are thermal energy reservoirs referred to as heat reservoirs?
They supply or absorb energy in the form of heat
What is the heat transfer associated with throttling valves?
Throttling valves are small devices so the flow through them is assumed to be adiabatic (q = 0) since there is not sufficient time or a large enough area for effective heat transfer to take place.
What is the objective of a refrigerator? How does it accomplish this objective?
To remove heat (QL ) from the refrigerated space *Requires a work input of Wnet,in to accomplish this objective
Why is a totally reversible process?
Totally reversible if it involves no irreversibilities within the system or surroundings.
True or False: No heat engine can convert all the heat it receives to work
True
True or False: The temperature of an ideal gas does not change during an throttling process.
True - Temp is constant because h = h(T)
True or False: The value of COPR can be greater than unity.
True - The amount of heat removed from the refrigerated space can be greater than the amount of work input.
What is the difference between a turbine and compressors, pumps, and fans?
Turbines produce power output whereas compressors, pumps, and fans require power input.
What is the work associated with nozzles and diffusers?
Typically involve no work (Wdot = 0) and any change in potential energy is negligible.
How do throttling valves differ from turbines?
Unlike turbines, they produce a pressure drop without involving any work.
How does a fluid flow into or out of a control volume?
Usually through pipes or ducts
Where are nozzles and diffusers commonly utilized?
Utilized in jet engines, rockets, spacecraft, and garden hoses
What is the most frequently used refrigeration cycle? What components are involved?
Vapor compression refrigeration cycle Involves compressor, condenser, expansion valve, and evaporator
Describe kinetic energy and velocity considerations in pipes and ducts.
Velocities involved in pipe or duct flow are relatively low and kinetic energy changes are insignificant. This is true when pipe or duct diameter is constant and heating effects are negligible. Kinetic energy changes may be significant for gas flow in ducts with variable cross sectional areas especially when compressibility effects are significant.
Why is velocity never uniform over a cross section of a pipe? What occurs instead?
Velocity is never uniform over a cross section of a pipe because of the no slip condition at the walls. Instead, the velocity varies from zero at the walls to some maximum value at or near centerline of the pipe.
What is volume flow rate and how is it calculated?
Volume of fluid flowing through a cross section per unit time Vdot = ∫VndAc = VavgAc = VAc
What are some examples of when heat transfer is desirable in pipes and ducts?
Water flow through the pipes in the furnace of a power plant, the flow of refrigerant in a freezer, and the flow in heat exchangers
What is the quantity Wdot for steady flow devices such as turbines, compressors, and pumps?
Wdot is the shaft power for these devices since these steady flow devices transmit power through a shaft
What is significant to note about Wdot in the energy balance equation for a steady flow system?
Wdot represents forms of work done per unit time that aren't included in the following: Since the control volume is constant for steady flow devices, no boundary work is involved. Also, the work required to push mass into and out of the control volume is taken care of by using enthalpies for the energy of fluid streams.
When does Wdot represent electrical work done per unit time?
When the control surface is crossed by electric wires, such as for an electric water heater.
When is the heat transfer rate 0 for a heat exchanger? When is it not 0?
When the entire heat exchanger is selected as the control volume, Qdot becomes 0 since the boundary for this case lies just beneath the insulation - little or no heat crosses the boundary. If only one of the fluids is selected as the control volume, then heat will cross this boundary as it flows from one fluid to the other and Qdot will not be 0. Qdot will be rate of heat transfer between the 2 fluids.
Why can't you just take the condenser out of the plant and save all the waste energy?
Without a heat rejection process in a condenser, the cycle cannot be completed. Cyclic devices such as steam power plants cannot run continuously unless the cycle is completed.
What is the conservation of energy principle for a cyclic device?
Wnet,in = QH - QL
How can you express the net work output and thermal efficiency relations for any heat engine?
Wnet,out = QH - QL thermal efficiency = Wnet,out / QH or thermal efficiency = 1 - (QL/QH)
Why are engineers interested in reversible processes?
Work producing devices (such as car engines and steam or gas turbines) deliver the most work, and work consuming devices (such as compressors, fans, and pumps) consume the least work when reversible processes are used
Are kinetic and potential energy negligible for throttling valves?
Yes Change in potential energy, if any, is very small. Even though exit velocity is considerably higher than inlet velocity, in many cases, the increase in kinetic energy is insignificant
Can the Carnot cycle be reversed? Why?
Yes - because it is a totally reversible cycle ,meaning that all the processes that comprise it can be reversed
Why is it convenient to use enthalpy instead of the internal energy to represent the energy of a flowing fluid?
You do not need to be concerned about flow work - the energy associated with pushing the fluid into or out of the control volume is automatically taken care of by enthalpy
A typical process involves interactions between __________________ and ______________________.
a system ; its surroundings
The net work output of a heat engine is ____________________ the amount of heat input, which means that _____________________.
always less than ; only part of the heat transferred to the heat engine is converted to work
Considering a fluid element of volume V : The fluid upstream forces the fluid element to enter the control. Therefore, it can be regarded as _______________________.
an imaginary piston
The __________________________ is one of the most fundamental principles in nature.
conservation of mass principle
How can the conservation of mass relation for a fixed control volume be expressed? What does this indicate?
d/dt ∫ρdV + ∫ρ(V*n)dA = 0 The time rate of change of mass within the control volume plus the net mass flow rate through the control surface is equal to 0
The differential mass flow rate of fluid flowing across a small area element dAc in a cross section of pipe is proportional to ________________________________________.
dAc itself, the fluid density, and the component of flow velocity normal to dAc δmdot = ρVndAc
The EER or COP of a refrigerator __________________ with decreasing refrigeration temperature.
decreases
The cross-sectional area of a nozzle __________________ in the flow direction for subsonic flows and _________________ for supersonic flows. The cross-sectional area of a diffuser _____________________ in the flow direction for subsonic flows and ________________ for supersonic flows.
decreases ; increases increases ; decreases
Work can be converted to heat _____________ and ___________, but converting heat to work ____________________________.
directly ; completely ; requires the use of special devices called heat engines
During a steady-flow process, the total amount of mass contained within a control volume __________________ change with time.
does not (mcv = constant)
The performance of air conditioners and heat pumps is often expressed in terms of the _____________________ or __________________.
energy efficiency ratio (EER) ; seasonal energy efficiency ratio (SEER)
How is the energy of a flowing fluid expressed on a unit mass basis?
energy_flowing_fluid = Pv + e = Pv + (u + ke + pe) But since Pv + u = h (enthalpy): energy_flowing_fluid = h + ke + pe = h + (V^2 / 2) + gz (kJ/kg)
Per the Kelvin-Planck statement, a heat engine is required to ?
exchange heat with a low temperature sink as well as a high temperature source to keep operating
A totally reversible process involves no ____________, no__________, and no ____________.
heat transfer through finite temp difference ; nonquasi equilibrium changes ; no friction or other dissipative effects
Heat engines operate between a __________________________ at ______________________ and a ________________________ at ___________________________.
high temperature medium (reservoir) ; temperature TH ; low temperature medium (reservoir) ; temperature TL
Heat is transferred from ___________________ to _______________________.
high temperature mediums ; low temperature mediums
All processes occuring in nature are ___________________.
irreversible
All physical and chemical systems exhibit energy interactions with their surroundings, but the amount of energy involved _________________________________________.
is equivalent to an extremely small mass compared to the system's total mass.
In a steam power plant, the condenser is the device where ___________________________________.
large quantities of waste heat is rejected to rivers, lakes, or the atmosphere
What is the equation for mass flow rate for incompressible flow or compressible flow where denisty is approximated as uniform across the cross sectional area?
mdot = ρVavgAc
How is the mass flow rate related to the volume flow rate?
mdot = ρVdot = Vdot/v where m is mass flow rate, V is volume flow rate, and v is specific volume
How is the conservation of mass principle expressed for single stream steady flow systems?
mdot1 = mdot2 => ρ1V1A1 = ρ2V2A2
How is the conservation of mass principle expressed in rate form?
mdotin - mdotout = dmcv / dt *For the special case of no mass crossing the control surface (i.e. the control volume is a closed system), the conservation of mass principle reduces to dmcv / dt = 0
What is the mass balance equation for a control volume?
mi - me = (m2 - m1)cv where i = inlet, e = exit, 1 = initial state, 2 = final state of control volume
In the mass balance equation for a control volume, when does mi equal 0? me? m1?
mi = 0 if no mass enters the control volume during the process me = 0 if no mass leaves m1 = 0 if control volume is initially evacuated
How is the mass balance for any system undergoing a process expressed?
min - mout = ▲msystem where ▲msystem = mfinal - minitial
What is the energy balance equation reduced to when the fluid experiences negligible changes in its kinetic and potential energies?
q - w = h2 - h1
The fluid properties at an inlet or exit _______________ during a steady flow process, but the properties __________________________ at different inlets and exits or ______________ over cross section of inlet or exit.
remain constant ; may be different ; vary
A heat pump will function at worst as a __________________.
resistance heater *Supply as much energy to the house as it consumes *Part of QH is lost to outside air through piping *COPHP may drop below unity when outside air temp is too low *When this happens, system switches to resistance heating mode
The most efficient cycles are ______________.
reversible cycles (cycles that consist entirely of reversible processes)
For reversible cycles, the heat transfer ratio QH/QL can be replaced by ___________________________.
the absolute temperature ratio TH/TL
In the net work output equation, Qout represents _______________. Is Qout ever 0?
the magnitude of the energy wasted in order to complete the cycle ; Qout is never 0
Most unsteady flow processes can be reasonably represented by ________________.
the uniform flow process
How do you express the thermal efficiency of any heat engine, reversible or irreversible?
thermal_efficiency = 1 - (QL/QH) *QH = heat transferred to heat engine from high temp reservoir at temp TH *QL = heat rejected to low temp reservoir at temp TL
How is the efficiency of a Carnot engine or any reversible heat engine?
thermal_efficiency_rev = 1 - (TL/TH)
How is the thermal efficiency of reversible heat engines expressed?
thermal_efficiency_rev = g(TH, TL) or QH / QL = f(TH, TL) since thermal_efficiency = 1 - (QL/QH) TH and TL are the temps of the high and low temperature reservoirs respectively
During an unsteady flow process, the energy content of a control volume changes with ________________. What does the magnitude of the change depend on?
time *Magnitude of change depends on amount of energy transfer across system boundaries as heat and work, as well as on the amount of energy transported into and out of the control volume by mass during the process.
What equation demonstrates how throttling affects fluid properties?
u1 + P1v1 = u2 + P2v2 OR internal energy + flow energy = constant
Most heat engines have efficiencies _____________________.
under 40%
The fluid properties at an opening are usually considered ____________ over the cross section, which allows the fluid properties at an inlet or exit to be specified by _____________________.
uniform (at some average value) ; the average single values
Every heat engine must ________________ by _________________________ in order to complete the cycle, even under idealized conditions.
waste some energy ; transferring it to a low temperature reservoir
For a closed system undergoing a cycle, the change in internal energy is ______________ and the net work output of the system is _____________________________________.
zero ; also equal to the net heat transfer to the system Wnet,out = Qin - Qout
The conservation of mass relations can be simplified to _____________ when the fluid is __________________, which is usually the case for liquids.
ΣVdotin = ΣVdotout => Vdot1 = Vdot2 => V1A1 = V2A2
How is the conservation of mass principle for a general steady flow system with multiple inlets and outlets expressed?
Σmdotin = Σmdotout
What are the differences between using d and δ to express differential quantities?
δ - used for quantities such as heat, work, and mass transfer that are path functions and have inexact differentials d - used for quantities such as properties that are point functions and have exact differentials