Entropy, Isentropic Relations, and Exergy Analysis
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Entropy, Isentropic Relations, and Exergy Analysis.
§6.1 Entropy as a state function
Unit 6, Lesson 1 — Entropy as a state function
Learning goals. Explain the physical meaning of the stated relationship; use the example to reconstruct a verifiable answer; identify at least two model limitations; and propose an independent check.
1. Physical question and conceptual model
Entropy change depends on the starting and ending equilibrium states. A reversible path may be used as a computational device even when the actual process is irreversible. Under a simple ideal-gas assumption at constant c_v, Δs=c_v ln(T2/T1)+R ln(v2/v1); the formula is not universal for condensing liquids.
Professional use. Trace the state measurements needed to determine s2−s1 using a property source. Avoid jumping from a property value to a performance guarantee: the former describes an assumed state, and the latter depends on losses, materials, reliability and operating limits.
2. Build the mathematical relationship
Governing statement: Δs=c_p ln(T2/T1)−R ln(p2/p1) for an ideal gas with constant cp.
Model qualification. The equation is meaningful only when its state and process assumptions are satisfied. Some equations are conservation balances that remain exact for their declared boundary; others are constitutive approximations, such as an ideal-gas relation, a constant heat capacity or an isentropic reference process. Determine which category this statement belongs to. Explain whether extra phenomena such as a moving boundary, leakage, heat loss, multiphase conditions, kinetic energy, electrical work or chemical reaction would add terms or require a different property source. If the process is transient, ask whether an accumulation term is missing.
3. Worked teaching example
At constant pressure, heating ideal-gas air from 300 K to 330 K with c_p=1.005 gives Δs≈0.0958 kJ/(kg K).
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
4. Failure analysis and engineering judgement
A tempting but incorrect shortcut: Declaring an actual frictional heating process reversible because a state-function calculation used a reversible integration path.
Investigate what this shortcut assumes about the device or material. Predict whether it would overstate useful work, misstate the phase, hide a heat leak or suppress a needed transport term. Estimate the direction of the bias before estimating its size. A numerical calculation that conserves energy can still violate the second law; similarly, a temperature prediction can be inconsistent with phase equilibrium. Test both conservation and state feasibility. Where the model is an ideal upper or lower bound, identify which side of the bound a real machine should occupy under comparable conditions.
Engineering context. Trace the state measurements needed to determine s2−s1 using a property source. A useful report would specify the relevant operating range, which properties are tabulated or calculated, and which assumptions are supported by evidence. It would not claim that an attractive textbook efficiency, coefficient of performance or output power proves achievable production performance.
5. Verification and measurement protocol
Design a simple check of entropy as a state function. Specify a control volume or control mass, boundary conditions, primary observations and sampling interval. Report whether the observation is direct (temperature, mass, voltage, volumetric flow), indirectly inferred (enthalpy, dryness fraction, exergy), or fitted from an empirical relation. Distinguish repeatability from model validity: a repeatable sensor can be wrongly calibrated, and a perfectly reproducible computer program can implement the wrong equation. Identify one test in which the idealization should perform reasonably, and a second test where a named assumption may break down. If you use fluid property tables or software, record its provenance, units, reference state and interpolation method.
6. Questions and answer criteria
Exercise A — Reconstruct. Reproduce the stated worked example with symbols, units and at least one limiting check. Answer criterion: obtain the stated value within rounding and explain each term in Δs=c_p ln(T2/T1)−R ln(p2/p1) for an ideal gas with constant cp.
Exercise B — Predict. Select one physically independent input, change it by 10%, and predict the response before calculation. Answer criterion: state whether a linear, reciprocal, logarithmic or state-dependent relationship is being used, and explain why it is valid over the selected interval.
Exercise C — Diagnose. Evaluate this proposed shortcut: "Declaring an actual frictional heating process reversible because a state-function calculation used a reversible integration path." Answer criterion: identify the missing assumption, specify a condition where the shortcut fails, and propose one measurement or alternate model that would expose the error.
7. Extended case and reproducible handover
Return to the condensing-steam turbine case that motivates this unit. The task is to compare ideal isentropic output with measured shaft power. Use this lesson's principle to create a two-column comparison between a minimal classroom calculation and a safer engineering estimate. The classroom side should contain only quantities supported by the basic model; the engineering side should add moisture at exit, flow measurement and environmental reference state. For each added quantity, say whether it is known, must be measured, can be estimated from trustworthy property data, or is impossible to infer from the current information. Where a value is unknown, retain a symbol or range instead of fabricating a precise number.
8. Closing self-test
Without viewing your notes, explain why the same physical device can be modeled with different boundaries, which quantities change accordingly and which conservation principles remain unchanged. Explain the relationship in your own words before quoting its symbols. If you cannot distinguish a property from a path function, or theoretical limit from verified behavior, revisit the model formulation rather than memorizing the numerical answer.
§6.2 Clausius inequality and entropy balance
Unit 6, Lesson 2 — Clausius inequality and entropy balance
Learning goals. Explain the physical meaning of the stated relationship; use the example to reconstruct a verifiable answer; identify at least two model limitations; and propose an independent check.
1. Physical question and conceptual model
A closed system satisfies ΔS=Σ∫δQ/T_boundary+S_gen, where T_boundary is the local absolute temperature at the heat transfer. For a cycle, ∮δQ/T≤0 under a consistent sign convention. Generation represents internally irreversible processes, not heat that crosses the boundary.
Professional use. Separate the transport accounting from the inequality; report any negative computed generation as a model or data warning. Avoid jumping from a property value to a performance guarantee: the former describes an assumed state, and the latter depends on losses, materials, reliability and operating limits.
2. Build the mathematical relationship
Governing statement: S_gen=ΔS−ΣQ_j/T_j≥0.
Model qualification. The equation is meaningful only when its state and process assumptions are satisfied. Some equations are conservation balances that remain exact for their declared boundary; others are constitutive approximations, such as an ideal-gas relation, a constant heat capacity or an isentropic reference process. Determine which category this statement belongs to. Explain whether extra phenomena such as a moving boundary, leakage, heat loss, multiphase conditions, kinetic energy, electrical work or chemical reaction would add terms or require a different property source. If the process is transient, ask whether an accumulation term is missing.
3. Worked teaching example
A closed system gains 0.50 kJ/K of entropy while receiving 100 kJ at a constant 400 K boundary; generation is 0.25 kJ/K.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
4. Failure analysis and engineering judgement
A tempting but incorrect shortcut: Forcing S_gen to zero without checking friction, gradients or mixing.
Investigate what this shortcut assumes about the device or material. Predict whether it would overstate useful work, misstate the phase, hide a heat leak or suppress a needed transport term. Estimate the direction of the bias before estimating its size. A numerical calculation that conserves energy can still violate the second law; similarly, a temperature prediction can be inconsistent with phase equilibrium. Test both conservation and state feasibility. Where the model is an ideal upper or lower bound, identify which side of the bound a real machine should occupy under comparable conditions.
Engineering context. Separate the transport accounting from the inequality; report any negative computed generation as a model or data warning. A useful report would specify the relevant operating range, which properties are tabulated or calculated, and which assumptions are supported by evidence. It would not claim that an attractive textbook efficiency, coefficient of performance or output power proves achievable production performance.
5. Verification and measurement protocol
Design a simple check of clausius inequality and entropy balance. Specify a control volume or control mass, boundary conditions, primary observations and sampling interval. Report whether the observation is direct (temperature, mass, voltage, volumetric flow), indirectly inferred (enthalpy, dryness fraction, exergy), or fitted from an empirical relation. Distinguish repeatability from model validity: a repeatable sensor can be wrongly calibrated, and a perfectly reproducible computer program can implement the wrong equation. Identify one test in which the idealization should perform reasonably, and a second test where a named assumption may break down. If you use fluid property tables or software, record its provenance, units, reference state and interpolation method.
6. Questions and answer criteria
Exercise A — Reconstruct. Reproduce the stated worked example with symbols, units and at least one limiting check. Answer criterion: obtain the stated value within rounding and explain each term in S_gen=ΔS−ΣQ_j/T_j≥0.
Exercise B — Predict. Select one physically independent input, change it by 10%, and predict the response before calculation. Answer criterion: state whether a linear, reciprocal, logarithmic or state-dependent relationship is being used, and explain why it is valid over the selected interval.
Exercise C — Diagnose. Evaluate this proposed shortcut: "Forcing S_gen to zero without checking friction, gradients or mixing." Answer criterion: identify the missing assumption, specify a condition where the shortcut fails, and propose one measurement or alternate model that would expose the error.
7. Extended case and reproducible handover
Return to the condensing-steam turbine case that motivates this unit. The task is to compare ideal isentropic output with measured shaft power. Use this lesson's principle to create a two-column comparison between a minimal classroom calculation and a safer engineering estimate. The classroom side should contain only quantities supported by the basic model; the engineering side should add moisture at exit, flow measurement and environmental reference state. For each added quantity, say whether it is known, must be measured, can be estimated from trustworthy property data, or is impossible to infer from the current information. Where a value is unknown, retain a symbol or range instead of fabricating a precise number.
8. Closing self-test
Without viewing your notes, explain why the same physical device can be modeled with different boundaries, which quantities change accordingly and which conservation principles remain unchanged. Explain the relationship in your own words before quoting its symbols. If you cannot distinguish a property from a path function, or theoretical limit from verified behavior, revisit the model formulation rather than memorizing the numerical answer.
§6.3 Isentropic reference devices and efficiency
Unit 6, Lesson 3 — Isentropic reference devices and efficiency
Learning goals. Explain the physical meaning of the stated relationship; use the example to reconstruct a verifiable answer; identify at least two model limitations; and propose an independent check.
1. Physical question and conceptual model
Reference turbine efficiency compares actual shaft-work-producing enthalpy drop with the drop for an isentropic outlet at the same exit pressure. A compressor comparison puts ideal enthalpy rise in the numerator. Losses make actual outlet entropy larger for an adiabatic single-inlet single-outlet machine, absent other effects.
Professional use. Explain why the reference exit pressure must be the same in both comparisons. Avoid jumping from a property value to a performance guarantee: the former describes an assumed state, and the latter depends on losses, materials, reliability and operating limits.
2. Build the mathematical relationship
Governing statement: η_t=(h1−h2_actual)/(h1−h2s).
Model qualification. The equation is meaningful only when its state and process assumptions are satisfied. Some equations are conservation balances that remain exact for their declared boundary; others are constitutive approximations, such as an ideal-gas relation, a constant heat capacity or an isentropic reference process. Determine which category this statement belongs to. Explain whether extra phenomena such as a moving boundary, leakage, heat loss, multiphase conditions, kinetic energy, electrical work or chemical reaction would add terms or require a different property source. If the process is transient, ask whether an accumulation term is missing.
3. Worked teaching example
If ideal turbine enthalpy drop is 200 kJ/kg and actual drop is 160 kJ/kg, η_t=80%.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
4. Failure analysis and engineering judgement
A tempting but incorrect shortcut: Using the turbine efficiency formula for a compressor, which can yield an apparent efficiency above unity.
Investigate what this shortcut assumes about the device or material. Predict whether it would overstate useful work, misstate the phase, hide a heat leak or suppress a needed transport term. Estimate the direction of the bias before estimating its size. A numerical calculation that conserves energy can still violate the second law; similarly, a temperature prediction can be inconsistent with phase equilibrium. Test both conservation and state feasibility. Where the model is an ideal upper or lower bound, identify which side of the bound a real machine should occupy under comparable conditions.
Engineering context. Explain why the reference exit pressure must be the same in both comparisons. A useful report would specify the relevant operating range, which properties are tabulated or calculated, and which assumptions are supported by evidence. It would not claim that an attractive textbook efficiency, coefficient of performance or output power proves achievable production performance.
5. Verification and measurement protocol
Design a simple check of isentropic reference devices and efficiency. Specify a control volume or control mass, boundary conditions, primary observations and sampling interval. Report whether the observation is direct (temperature, mass, voltage, volumetric flow), indirectly inferred (enthalpy, dryness fraction, exergy), or fitted from an empirical relation. Distinguish repeatability from model validity: a repeatable sensor can be wrongly calibrated, and a perfectly reproducible computer program can implement the wrong equation. Identify one test in which the idealization should perform reasonably, and a second test where a named assumption may break down. If you use fluid property tables or software, record its provenance, units, reference state and interpolation method.
6. Questions and answer criteria
Exercise A — Reconstruct. Reproduce the stated worked example with symbols, units and at least one limiting check. Answer criterion: obtain the stated value within rounding and explain each term in η_t=(h1−h2_actual)/(h1−h2s).
Exercise B — Predict. Select one physically independent input, change it by 10%, and predict the response before calculation. Answer criterion: state whether a linear, reciprocal, logarithmic or state-dependent relationship is being used, and explain why it is valid over the selected interval.
Exercise C — Diagnose. Evaluate this proposed shortcut: "Using the turbine efficiency formula for a compressor, which can yield an apparent efficiency above unity." Answer criterion: identify the missing assumption, specify a condition where the shortcut fails, and propose one measurement or alternate model that would expose the error.
7. Extended case and reproducible handover
Return to the condensing-steam turbine case that motivates this unit. The task is to compare ideal isentropic output with measured shaft power. Use this lesson's principle to create a two-column comparison between a minimal classroom calculation and a safer engineering estimate. The classroom side should contain only quantities supported by the basic model; the engineering side should add moisture at exit, flow measurement and environmental reference state. For each added quantity, say whether it is known, must be measured, can be estimated from trustworthy property data, or is impossible to infer from the current information. Where a value is unknown, retain a symbol or range instead of fabricating a precise number.
8. Closing self-test
Without viewing your notes, explain why the same physical device can be modeled with different boundaries, which quantities change accordingly and which conservation principles remain unchanged. Explain the relationship in your own words before quoting its symbols. If you cannot distinguish a property from a path function, or theoretical limit from verified behavior, revisit the model formulation rather than memorizing the numerical answer.
§6.4 work opportunity
Unit 6, Lesson 4 — Exergy of heat and useful-work opportunity
Learning goals. Explain the physical meaning of the stated relationship; use the example to reconstruct a verifiable answer; identify at least two model limitations; and propose an independent check.
1. Physical question and conceptual model
Exergy depends on a declared reference environment. For heat transfer from a reservoir at T_s, the ideal maximum useful work fraction relative to ambient T_0 is 1−T_0/T_s. As the source temperature approaches ambient, useful-work potential approaches zero even though the heat energy remains finite.
Professional use. Record reference temperature and whether ambient conditions vary during operation. Avoid jumping from a property value to a performance guarantee: the former describes an assumed state, and the latter depends on losses, materials, reliability and operating limits.
2. Build the mathematical relationship
Governing statement: Ex_Q=Q(1−T0/Ts).
Model qualification. The equation is meaningful only when its state and process assumptions are satisfied. Some equations are conservation balances that remain exact for their declared boundary; others are constitutive approximations, such as an ideal-gas relation, a constant heat capacity or an isentropic reference process. Determine which category this statement belongs to. Explain whether extra phenomena such as a moving boundary, leakage, heat loss, multiphase conditions, kinetic energy, electrical work or chemical reaction would add terms or require a different property source. If the process is transient, ask whether an accumulation term is missing.
3. Worked teaching example
For 100 kJ supplied at 500 K to an environment at 300 K, heat exergy is 40 kJ.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
4. Failure analysis and engineering judgement
A tempting but incorrect shortcut: Treating all kilojoules of low-grade waste heat as equal to shaft-work kilojoules.
Investigate what this shortcut assumes about the device or material. Predict whether it would overstate useful work, misstate the phase, hide a heat leak or suppress a needed transport term. Estimate the direction of the bias before estimating its size. A numerical calculation that conserves energy can still violate the second law; similarly, a temperature prediction can be inconsistent with phase equilibrium. Test both conservation and state feasibility. Where the model is an ideal upper or lower bound, identify which side of the bound a real machine should occupy under comparable conditions.
Engineering context. Record reference temperature and whether ambient conditions vary during operation. A useful report would specify the relevant operating range, which properties are tabulated or calculated, and which assumptions are supported by evidence. It would not claim that an attractive textbook efficiency, coefficient of performance or output power proves achievable production performance.
5. Verification and measurement protocol
Design a simple check of exergy of heat and useful-work opportunity. Specify a control volume or control mass, boundary conditions, primary observations and sampling interval. Report whether the observation is direct (temperature, mass, voltage, volumetric flow), indirectly inferred (enthalpy, dryness fraction, exergy), or fitted from an empirical relation. Distinguish repeatability from model validity: a repeatable sensor can be wrongly calibrated, and a perfectly reproducible computer program can implement the wrong equation. Identify one test in which the idealization should perform reasonably, and a second test where a named assumption may break down. If you use fluid property tables or software, record its provenance, units, reference state and interpolation method.
6. Questions and answer criteria
Exercise A — Reconstruct. Reproduce the stated worked example with symbols, units and at least one limiting check. Answer criterion: obtain the stated value within rounding and explain each term in Ex_Q=Q(1−T0/Ts).
Exercise B — Predict. Select one physically independent input, change it by 10%, and predict the response before calculation. Answer criterion: state whether a linear, reciprocal, logarithmic or state-dependent relationship is being used, and explain why it is valid over the selected interval.
Exercise C — Diagnose. Evaluate this proposed shortcut: "Treating all kilojoules of low-grade waste heat as equal to shaft-work kilojoules." Answer criterion: identify the missing assumption, specify a condition where the shortcut fails, and propose one measurement or alternate model that would expose the error.
7. Extended case and reproducible handover
Return to the condensing-steam turbine case that motivates this unit. The task is to compare ideal isentropic output with measured shaft power. Use this lesson's principle to create a two-column comparison between a minimal classroom calculation and a safer engineering estimate. The classroom side should contain only quantities supported by the basic model; the engineering side should add moisture at exit, flow measurement and environmental reference state. For each added quantity, say whether it is known, must be measured, can be estimated from trustworthy property data, or is impossible to infer from the current information. Where a value is unknown, retain a symbol or range instead of fabricating a precise number.
8. Closing self-test
Without viewing your notes, explain why the same physical device can be modeled with different boundaries, which quantities change accordingly and which conservation principles remain unchanged. Explain the relationship in your own words before quoting its symbols. If you cannot distinguish a property from a path function, or theoretical limit from verified behavior, revisit the model formulation rather than memorizing the numerical answer.
§6.5 Exergy destruction and practical optimization
Unit 6, Lesson 5 — Exergy destruction and practical optimization
Learning goals. Explain the physical meaning of the stated relationship; use the example to reconstruct a verifiable answer; identify at least two model limitations; and propose an independent check.
1. Physical question and conceptual model
Entropy generation destroys the ability to perform useful work: Ex_destroyed=T0 S_gen. A component may conserve total energy while destroying exergy. A design improvement that transfers heat closer to a reversible temperature profile can reduce lost work but require more exchanger area and capital expense.
Professional use. Make a trade-off table: exergy saved, added area, added pressure loss and maintenance burden. Avoid jumping from a property value to a performance guarantee: the former describes an assumed state, and the latter depends on losses, materials, reliability and operating limits.
2. Build the mathematical relationship
Governing statement: Ex_destroyed=T0 S_gen.
Model qualification. The equation is meaningful only when its state and process assumptions are satisfied. Some equations are conservation balances that remain exact for their declared boundary; others are constitutive approximations, such as an ideal-gas relation, a constant heat capacity or an isentropic reference process. Determine which category this statement belongs to. Explain whether extra phenomena such as a moving boundary, leakage, heat loss, multiphase conditions, kinetic energy, electrical work or chemical reaction would add terms or require a different property source. If the process is transient, ask whether an accumulation term is missing.
3. Worked teaching example
At T0=300 K and S_gen=0.20 kJ/K, destroyed exergy is 60 kJ.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
4. Failure analysis and engineering judgement
A tempting but incorrect shortcut: Optimizing exergy efficiency alone while ignoring pressure drop, cost or mechanical reliability.
Investigate what this shortcut assumes about the device or material. Predict whether it would overstate useful work, misstate the phase, hide a heat leak or suppress a needed transport term. Estimate the direction of the bias before estimating its size. A numerical calculation that conserves energy can still violate the second law; similarly, a temperature prediction can be inconsistent with phase equilibrium. Test both conservation and state feasibility. Where the model is an ideal upper or lower bound, identify which side of the bound a real machine should occupy under comparable conditions.
Engineering context. Make a trade-off table: exergy saved, added area, added pressure loss and maintenance burden. A useful report would specify the relevant operating range, which properties are tabulated or calculated, and which assumptions are supported by evidence. It would not claim that an attractive textbook efficiency, coefficient of performance or output power proves achievable production performance.
5. Verification and measurement protocol
Design a simple check of exergy destruction and practical optimization. Specify a control volume or control mass, boundary conditions, primary observations and sampling interval. Report whether the observation is direct (temperature, mass, voltage, volumetric flow), indirectly inferred (enthalpy, dryness fraction, exergy), or fitted from an empirical relation. Distinguish repeatability from model validity: a repeatable sensor can be wrongly calibrated, and a perfectly reproducible computer program can implement the wrong equation. Identify one test in which the idealization should perform reasonably, and a second test where a named assumption may break down. If you use fluid property tables or software, record its provenance, units, reference state and interpolation method.
6. Questions and answer criteria
Exercise A — Reconstruct. Reproduce the stated worked example with symbols, units and at least one limiting check. Answer criterion: obtain the stated value within rounding and explain each term in Ex_destroyed=T0 S_gen.
Exercise B — Predict. Select one physically independent input, change it by 10%, and predict the response before calculation. Answer criterion: state whether a linear, reciprocal, logarithmic or state-dependent relationship is being used, and explain why it is valid over the selected interval.
Exercise C — Diagnose. Evaluate this proposed shortcut: "Optimizing exergy efficiency alone while ignoring pressure drop, cost or mechanical reliability." Answer criterion: identify the missing assumption, specify a condition where the shortcut fails, and propose one measurement or alternate model that would expose the error.
7. Extended case and reproducible handover
Return to the condensing-steam turbine case that motivates this unit. The task is to compare ideal isentropic output with measured shaft power. Use this lesson's principle to create a two-column comparison between a minimal classroom calculation and a safer engineering estimate. The classroom side should contain only quantities supported by the basic model; the engineering side should add moisture at exit, flow measurement and environmental reference state. For each added quantity, say whether it is known, must be measured, can be estimated from trustworthy property data, or is impossible to infer from the current information. Where a value is unknown, retain a symbol or range instead of fabricating a precise number.
8. Closing self-test
Without viewing your notes, explain why the same physical device can be modeled with different boundaries, which quantities change accordingly and which conservation principles remain unchanged. Explain the relationship in your own words before quoting its symbols. If you cannot distinguish a property from a path function, or theoretical limit from verified behavior, revisit the model formulation rather than memorizing the numerical answer.
Step-by-Step Engineering Thermodynamics Solutions
Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.
At constant pressure, heating ideal-gas air from 300 K to 330 K with c_p=1.005 gives Δs≈0.0958 kJ/(kg K).
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
A closed system gains 0.50 kJ/K of entropy while receiving 100 kJ at a constant 400 K boundary; generation is 0.25 kJ/K.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
If ideal turbine enthalpy drop is 200 kJ/kg and actual drop is 160 kJ/kg, η_t=80%.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
For 100 kJ supplied at 500 K to an environment at 300 K, heat exergy is 40 kJ.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.
At T0=300 K and S_gen=0.20 kJ/K, destroyed exergy is 60 kJ.
Interpretive check. Does the result increase or decrease when the principal driving condition becomes stronger? Does the prediction approach a sensible limit when the temperature difference, flow rate, state change or relevant force approaches zero? Such limiting tests are not substitutes for a measurement, but they are effective at rejecting a broken model before the expensive stage of building apparatus or selecting equipment.