Thermodynamics
Dynamis
"Power"
Sensible Heat
'Regular' addition of energy with no phase change... But you can measure (i.e. sense) a temperature change.
Fluids
- essentially incompressible. - variation of density with pressure is negligible.
Pressures in a Fluid
- same magnitude in all directions. - varies with depth due to 'weight above'.
What is the lowest temperature on a Celsius scale?
-273.15°C 0 K (Absolute zero)
What are the different mechanisms for transferring energy to or from a control volume?
-Heat (requires a temperature gradient) -Work -Mass transfer
Factors that cause a process to be irreversible:
-Heat transfer thru a finite temperature difference -Friction -Unrestrained expansion of gas -Mixing of fluids -Inelastic deformation of a solid -Chemical reactions -Electrical resistance -Noise
Steady Flow Devices
-Nozzles & Diffusers -Compressors & Turbines -Throttling Valves -Mixing Chambers -Heat Exchangers
Entropy
-a measure of disorder within a system -chaos -a measure of molecular randomness ... entropy increases as temperature increases The total amount of entropy in the universe is always increasing.
Water freezes @...
0.01°C or 32.02°F (@ 1ATM)
Using the Compressibility Factor (Z)
1. Lookup properties for substance (R, Pcrit, Tcrit) 2. Determine specific volume v-ideal, based on ideal gas. 3. Determine P-R & T-R 4. Lookup Z on chart (Figure A-28) 5. Finally determine v-actual = Z * v-ideal
Enthalpy is used when...
1. Mass crosses a system boundary at a specified pressure. 2. If a fixed mass undergoes a constant pressure volume change.
Carnot Principles
1. The efficiency of an irreversible (i.e. real) heat engine is always less than a reversible one operating between the same two thermal reservoirs. 2. The efficiency of all reversible heat engines operating between the same two thermal reservoirs is the same.
H2O
100% Saturated Vapour - any additional energy will increase temperature (& volume).
Water boils @...
100°C or 212.00°F (@ 1ATM)
1 ATM
101.325 kPa
Thermal (Energy) Reservoir
A body that can supply or absorb a relatively large amount of heat without undergoing a change in temperature. Two basic reservoir types: SOURCE - a reservoir that supplies energy in the form of heat. SINK - a reservoir that absorbs energy in the form of heat.
Heat
A form of energy that can be transferred from one system to another based on a temperature differential. The amount of energy transfer can be predicted by the First Law.
Temperature
A measure of the kinetic energy of a substance at the atomic level.
Isothermal Process
A process during which temperature remains constant.
Isobaric Process
A process during which the pressure remains constant.
Isochoric Process
A process during which the specific volume remains constant.
'Iso' (prefix)
A property remains constant.
Isentropic Processes
A reversible adiabatic process (from a systems perspective) will be isentropic ... however An isentropic process (from a systems perspective) is not necessarily a reversible adiabatic process - a real process will generate entropy ... BUT entropy may be transferred out of the 'system' via heat ... so the net could appear zero
The difference between a Saturated Liquid and a Compressed Liquid.
A saturated liquid is a liquid that is about to vaporize, that the addition of any more energy will start vaporization; otherwise if it's not about to vaporize, it's a compressed liquid.
Energy Interactions
A system's energy level can only change if there is an interaction with the environment thru: 1. exchange of heat 2. a work interaction 3. mass exchange - energy exchange occurs at the system boundary.
The difference between a Saturated Vapour and a Superheated Vapour
A vapour that is about to condense is a saturated vapour; otherwise if it's not about to condense, it's a superheated vapour.
Simple Compressible
Absence of external forces such as: - electrical - magnetic - gravitational - motion - surface tension
Maximum Work Output
Adiabatic (Q=0) Isentropic (s2=s1) Use energy expression to find Wout_max
What is the Principle of Corresponding States?
All gases when normalized relative to their critical point temperature and pressure deviate from the ideal gas law in a similar manor. Therefore the behaviour can be plotted on a general compressibility chart.
Coefficients of Performance
Analogous to thermal efficiency, but can be greater than 1.
Property
Any characteristic of a system, (P, T, V, m).
When to use IDEAL Gas
At low pressure (P-R << 1) gases behave as ideal regardless of temperature... we want P << Pcrit OR At high temperatures (T-R > 2) gases behave as Ideal... we want T > 2 x Tcrit Biggest deviation from Ideal occurs when gas is near the critical point.
Under what conditions is the Ideal-gas assumption suitable for real gases?
At low pressures and high temperatures relative to the substances critical point.
Open Systems
Can have all three: heat, work and/or mass
Carnot Cycle
Carnot Cycles: -models a reversible (theoretically ideal) heat engine & heat pump -provides the upper limit on efficiency or coefficient of performance (to allow evaluation of real systems) -named after Sadi Carnot, 1824 Carnot Cycles employ four idealized reversible processes: -two are isothermal (constant temperature) -two are adiabatic (no heat transfer) -insulation is removed during the heat exchange process
Process
Changing from one state to another.
Closed Systems
Characterized by: - no mass exchange across the system boundary. - work interactions and thermal interactions allowed.
Heat transfer occurs by three methods:
Conduction: between two substances that are in direct contact. Convection: conduction from a solid to a fluid that is in motion, the fluid distributes the energy to other solids. Radiation: emission of electromagnetic waves (photons)
First Law of Thermodynamics
Conservation of energy: energy cannot be created or destroyed, it can only change from one form to another.
Heat Engines
Converts heat to work. Heat Engines: -receive heat from a high temperature source -convert part of this heat to work (usually turning a shaft) -reject the rest of the heat to a low temperature sink -operate on a cycle
Specific Heats
Cp is always greater than Cv. -if the system is allowed to expand (to maintain constant pressure) more energy is required to offset the expansion work (since the particles are further apart)
Specific Heats
Cv = specific heat at constant volume. (based on the energy required to raise the substance by one degree when volume is maintained constant) Cp = specific heat at constant pressure. (based on the energy required to raise the substance by one degree when pressure is maintained constant)
Heat Transfer
Deals with determining the rate of energy transfer.
Extensive Property
Depends on size/extent of system, (m, V).
Nozzle
Device that increases fluid velocity. - pressure decreases
Diffuser
Device that increases pressure. -fluid velocity decreases
Intensive/Extensive Test
Divide the system in half: - intensive properties don't change. - extensive properties will be halved.
Refrigeration Efficiency Limits
Efficiency of refrigeration and heat pump cycles decrease as TL decreases ... it requires more work to absorb heat from lower temperature media.
LHS =
Ein - Eout -> (Qin - Qout) + (Win - Wout) + (Emass_in - Emass_out)
RHS
Energy Storage Mechanisms
Latent Heat of Fusion
Energy absorbed during melting. Energy released during freezing.
Latent Heat of Vaporization
Energy absorbed during vaporization. Energy released during condensation.
Conservation of Energy
Energy must balance: L.H.S. - deals with energy interactions R.H.S. - deals with storage mechanisms
Rate
Energy per unit time
Latent Heat
Energy released/absorbed during a phase change (no corresponding change in temperature).
1 Calorie
Energy required to raise 1 gram of water (@ 15°C) by 1°C.
1 British Thermal Unit
Energy required to raise 1-lbm of water (@ 68°F) by 1°F.
Entropy Transfer in Open Systems
Entropy is NOT transferred with work crossing a system boundary ... work is highly organized
Entropy
Entropy is a property. -can be one of the two independent intensive properties needed to complete a state description.
Moving Boundary Work
Expansion -> V2 > V1 so change in V is positive... Pdv is positive Compression -> V2 < V1 so change in V is negative... Pdv is negative
Moving Boundary Work
Expansion or compression of volume of gas entails mechanical work... we call this moving boundary work.
Throttling Valve
Flow restricting devices... Pressure is reduced without doing useful work or causing velocity to increase substantially. -Inlet and outlet areas adjusted to compensate for volume expansion. dW=0 dPE=0 dKE=0 dQ~0 (adiabatic: small area & contact time) -Based on the above conditions, Enthalpy is constant. h2=h1 Known as "isenthalpic"
Steady Flow Systems
Fluid Properties: -can change from point to point within the control volume, but at any given location, the properties do not change in time (hence they are steady)
Turbine
Fluid passing through the device does work on the blades which turn the output shaft.
Critical Point
For H2O: Tcr: 374°C Pcr: 22MPa vcr: 0.003 m^3/kg (~300 kg/m^3) A saturation line is non-existent. Saturated liquid and Saturated vapour points are equivalent. At pressures above the critical point, there is no distinct phase change process. - specific volume increases continuously. - only one phase present. - it eventually resembles a vapour.
Specific Heats
For Ideal Gases and Incompressible substances, Specific heat values are dependent on temperature. Cv=Cv(T) Cp=Cp(T)
Work
Force acting through a distance. - moving a system boundary (i.e. pressure-volume work) - 'forcing' mass across the pressure at a boundary - 'forcing' an electron across a boundary (electrical work) - turning a shaft (i.e. turbine, pump, motor) - compressing a spring
Pressure
Force exerted by a fluid per unit area.
Common measured pressures use atmospheric pressure as the zero reference
Gauge Pressure: positive pressures. Vacuum Pressure: pressures lower than atmospheric.
Therme
Greek for "heat".
Process vs. Properties
Heat and Work are energy transfer mechanisms - require interaction between the system and the surroundings - they are boundary phenomena - they are associated with a process, not a state - the process path is critical for a evaluation of energy exchange Properties (temperature, pressure, etc.) are point functions - they depend only on the state - they do not depend on how you arrived at that state ...'Internal Energy', U is a property
Entropy
If the cycle is perfect: (Q/T)rev =0 If the cycle is not perfect: (Q/T)real <0
When is the energy crossing the boundaries of a closed system heat and when is it work?
If the energy is transferred by virtue of a temperature difference between the boundary surface and the environment, then the transfer method is heat. All other energy transfer occurs by work.
T-S Plot
If the process is internally reversible: area under the T-S curve represents the heat transfer dS = dQ/T If the process is not internally reversible: area is meaningless.
Zeroth Law of Thermodynamics
If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other.
Intensive Property
Independent of size of system, (T, P, density).
Entropy and Open Systems
Isentropic processes determine the limits for adiabatic devices such as: -nozzles -diffusers -turbines -compressors -throttling valves
Entropy: Special Case
Isothermal heat transfer is an internally reversible process. dS can be +ve or -ve based on the direction of heat flow
Kelvin-Planck Statement of the 2nd Law
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.
Clausius Statement of the 2nd Law
It is impossible to construct a device that operates in a cycle and produces no other effect than the transfer of heat from a lower-temperature body to a higher-temperature body.
1 Watt =
J/s
Enthalpy
Mass exchange across a system boundary, (@ a specified pressure). - Therefore 'work' is performed. - The mass also carries in internal energy.
Steady
No change with time.
Isolated System
No mass or energy transfer.
Does the reference point selected for the properties of a substance have any affect on the thermodynamic analysis?
No. We are typically interested in differences, changes from state to state.
Entropy and the 2nd Law
Only processes that result in an increase of entropy are physically possible; entropy is always increasing. -entropy is not conserved -real process will 'generate' entropy -consider both system and the surroundings
Specific Heats for Ideal Gases
Over small temperature delta's: -approximate the C(T) curve with a straight line -if specific heat comes from tables values use temperature to interpolate data ...if required, assume T2 ... do calc's ... refine
Superheated Vapour
P < Psat @ a given T T > Tsat @ a given P v > vg @ given P or T u > ug @ given P or T h > hg @ given P or T
Compressed Liquid
P > Psat @ a given T T < Tsat @ a given P v < vf @ given P or T u < uf @ given P or T h < hf @ given P or T
Specific Quantities
Per unit mass
How are reduced temperature and pressure defined?
Pr= P/Pcrit Tr= T/Tcrit
Absolute Pressure
Pressure is relative to a perfect vacuum.
Adiabatic
Process with no heat transfer. How? - make it difficult for heat to flow... insulate the system boundary - no change in Temp with the environment... remove the driving force for heat transfer.
LHS =
Qnet - Wnet
System
Quantity of matter or a region of space chosen for study.
Compressors & Turbines
Q~0 KE~0 PE~0
Nozzles & Diffusers
Q~0 W=0 PE~0 KE (cannot=0)
Throttling Processes
R-134a: temperature decreases during throttling ... the throttling valve is called an expansion valve, hinting that refrigerant volume increases significantly during throttling. Ideal Gases: have no change in temperature ... h=f(T) but h1=h2 so T1=T2 Hydrogen: increases in temperature during throttling.
Quality
Ratio of mass of vapour to total mixture mass. X = m-vapour/m-total
Irreversible Processes
Real Processes: ... cannot reverse themselves spontaneously and restore the system and surroundings to their initial state. -We can restore a system to it's original state... BUT it will cost us; the surroundings will not be in their original state.
Refrigerators & Heat Pumps
Refrigerator - heat absorbed from 'cold space' has value Heat Pump - heat rejected to 'warm space' has value
Closed Systems
Restricted to heat and/or work interactions only.
Reversible Process
Reversible processes (an idealized process): ... if you ran the process in reverse, the system and the surrounding would be restored to their original states. -this would yield the theoretical limits on process efficiency, i.e. the maximum efficiency of a heat engine or refrigeration cycle. -reversible processes do not actually occur
Thermodynamics
Science that deals with: Interrelationship between heat, work, and energy in transport, transfer, and conversion processes. - Predicts the maximum energy that may be extracted and how efficiently it may be done for a particular situation.
State
Set of properties with fixed values that completely describe the "state of the system". - change one of these values -> change the state.
Entropy Generation
Sgen - is NOT a property ... it depends on the process - is ALWAYS positive ... irreversibilities always increase entropy - Sgen < 0 is NOT possible The 'system' entropy may decrease BUT the net entropy change of 'system' and 'surroundings' will increase
Heat Engine Efficiency Limits
Since all Carnot heat engines have the same efficiency, the efficiency must be a function of the reservoir temperature: nth,rev =1-(TL/TH) -efficiency can be improved by increasing TH or decreasing TL -materials often limit TH -availability of cooling media limits TL
Second Law of Thermodynamics:
States that energy has quality. - Processes or transformations will only naturally occur in one direction (the direction of decreasing quality).
Pure Substance
Substance with same chemical composition throughout. - All pure substances exhibit the same general phase behaviour.
Gas
Superheated Vapour
Closed System
System that contains a fixed amount of mass. Referred to as "control mass" 1. mass cannot cross the boundary. 2. Energy can cross the boundary. 3. Volume does not have to be fixed.
Open System
System where mass and energy can cross the boundary. - occupy a region in space referred to as the "control volume". The boundary of the control volume is the "control surface".
Joules-Thompson Effect
Temperature change due to throttling.
In the absence of Compressed Liquid Tables, how is Specific Volume of a Compressed Liquid at a given P and T determined?
Temperature has more effect than pressure so an estimate of the specific volume is made by using the vf (saturated liquid state data) as if the liquid was saturated at the specified temperature.
Saturated Liquid-Vapour Mixture
Temperature will remain constant until all the liquid has vaporized, (provided pressure is constant). - volume will increase - Liquid & Vapour co-exist in equilibrium. ...with the addition of energy, the percentage of vapour in the saturated liquid-vapour mixture will increase.
Specific Heat
The amount of energy required to raise the temperature of a unit mass of a substance by 1°.
Isentropic Processes
The best case will occur if the process was reversible... Isentropic processes are used as benchmarks to establish the limits for real processes.
Consequences of The First Law
The energy of a system only changes if the state changes... energy is a property of a system.
Working Fluid
The media that undergoes the cycle in a heat engine. -high heat capacities are desirable (H2O) -easy to handle and plentiful -chemically stable/compatible with other system components
Saturation Pressure
The pressure at which a pure substance changes phase for a given temperature.
Boundary
The real or imaginary surface that separates the system from it's surroundings. - Can be fixed or movable.
(Process) Path
The series of intermediate states that a system goes through.
State Postulate
The state of a simple compressible system is completely specified by two independent, intensive properties.
Saturation Temperature
The temperature at which a pure substance changes phase for a given pressure.
Entropy and the Third Law
Third Law of Thermodynamics: "Entropy of a pure (crystalline) substance at a temperature of absolute zero is zero as there is no uncertainty about the state of the molecules." In general, entropy is lowest in cold solids and highest in hot gases.
Heat Exchangers
Two moving fluids exchange heat without directly mixing. -Heat (Q) flows thru walls to lower temperature fluid -Mass flow of each fluid is constant W=0 PE~0 KE~0 -Heat transfer to the external environment is usually minimized with insulation -Counterflow: fluids flow in opposite directions to help maintain constant dT
Mixing Chamber
Two or more streams are brought into direct contact. dQ~0 (adiabatic, small area) dW=0 dP=0 dKE~0
Polytropic Equation for Ideal Gas
Wb =mR(T2-T1)/(1-n)
Polytropic Equation for Isothermal Ideal Gas
Wb=PVln(V2/V1)
Cycle
When a system returns to the initial state.
Work Output from a Heat Engine
Wnet_out = Qin-Qout
Compressor
Working fluid gains energy due to mechanical work input.
Is it possible to have water vapour @ -10°C?
Yes. See Table A-8: vapour and solid can co-exist at the T's and P's given on this chart.
Entropy Defined
dS=(Q/T)rev
