First Law of Thermodynamics and Closed-System Energy Analysis
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of First Law of Thermodynamics and Closed-System Energy Analysis.
§3.1 law sign conventions
Unit 3, Lesson 1 — Energy bookkeeping and first-law sign conventions
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
System energy includes internal, kinetic and gravitational potential terms. Positive heat Q entering the system and positive work W done by the system yield ΔE=Q−W. A convention that counts work done on the system positively is valid only if used consistently. Chemical and nuclear terms require appropriate system models beyond a simple sensible-heat balance.
Professional use. Draw heat and work arrows on the closed boundary and annotate the resulting ΔU sign. 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: ΔU=Q−W if ΔKE and ΔPE are negligible.
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 gas receives Q=120 kJ and expands doing W=35 kJ; its internal energy increases by 85 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: Switching work sign conventions midway through the calculation.
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. Draw heat and work arrows on the closed boundary and annotate the resulting ΔU sign. 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 energy bookkeeping and first-law sign conventions. 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 ΔU=Q−W if ΔKE and ΔPE are negligible.
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: "Switching work sign conventions midway through the calculation." 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 instrumented piston cylinder case that motivates this unit. The objective is to infer boundary work and heating from recorded p–V–T histories. 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 hysteresis, friction and small-scale heat leaks. 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.
§3.2 boundary work
Unit 3, Lesson 2 — Moving-boundary work
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
For a simple compressible system evolving quasistatically, differential displacement work equals system pressure times volume change. Its integral depends on the p–V path. Free expansion into a vacuum does not perform boundary work against an external resisting pressure, even if system volume grows.
Professional use. Plot two paths connecting the same endpoints and explain why W differs while ΔU does not. 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: W_b=∫p dV.
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 p=200 kPa constant and V rising by 0.030 m³, W_b=6.0 kJ done by the gas.
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 p1(V2−V1) for an arbitrary curved polytropic 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. Plot two paths connecting the same endpoints and explain why W differs while ΔU does not. 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 moving-boundary work. 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 W_b=∫p dV.
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 p1(V2−V1) for an arbitrary curved polytropic 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 instrumented piston cylinder case that motivates this unit. The objective is to infer boundary work and heating from recorded p–V–T histories. 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 hysteresis, friction and small-scale heat leaks. 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.
§3.3 Internal energy, heat capacities and ideal gases
Unit 3, Lesson 3 — Internal energy, heat capacities and ideal gases
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
For an ideal gas, internal energy depends on temperature alone and du=c_v(T)dT. Enthalpy also depends only on temperature for this model, with dh=c_p(T)dT and c_p−c_v=R. Constant-property approximations simplify short intervals but can become inaccurate across broad temperature spans.
Professional use. State which heat capacity is appropriate and whether measured temperature changes are spatially uniform. 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: ΔU≈m c_v(T2−T1).
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 2 kg of an ideal gas with c_v=0.718 kJ/(kg K) heated 50 K, ΔU≈71.8 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: Using c_p to compute closed-tank internal-energy change without checking the model.
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. State which heat capacity is appropriate and whether measured temperature changes are spatially uniform. 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 internal energy, heat capacities and ideal gases. 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 ΔU≈m c_v(T2−T1).
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 c_p to compute closed-tank internal-energy change without checking the model." 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 instrumented piston cylinder case that motivates this unit. The objective is to infer boundary work and heating from recorded p–V–T histories. 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 hysteresis, friction and small-scale heat leaks. 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.
§3.4 Polytropic processes and isothermal limits
Unit 3, Lesson 4 — Polytropic processes and isothermal limits
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 polytropic model imposes pV^n=constant over a specified path. Its exponent is a process description, not a universal gas property. For n≠1, boundary work is (p2V2−p1V1)/(1−n). For a quasistatic ideal gas at constant temperature, n=1 and work takes a logarithmic form.
Professional use. Check whether fitted n changes when leakage, heat transfer or friction varies. 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: W=(p2V2−p1V1)/(1−n), n≠1.
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 p1=200 kPa, V1=0.10 m³, V2=0.20 m³ and n=1.3, p2≈81.2 kPa and W≈12.5 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: Confusing polytropic exponent n with ratio of specific heats k=c_p/c_v.
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. Check whether fitted n changes when leakage, heat transfer or friction varies. 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 polytropic processes and isothermal limits. 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 W=(p2V2−p1V1)/(1−n), n≠1.
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: "Confusing polytropic exponent n with ratio of specific heats k=c_p/c_v." 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 instrumented piston cylinder case that motivates this unit. The objective is to infer boundary work and heating from recorded p–V–T histories. 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 hysteresis, friction and small-scale heat leaks. 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.
§3.5 Cycles, calorimetry and experimental balances
Unit 3, Lesson 5 — Cycles, calorimetry and experimental balances
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
For a complete closed-system cycle ΔU=0, so net heat equals net work when kinetic and potential terms return to their initial states. Real calorimeters account for vessel heat capacity and losses. A temperature plateau during phase change may reflect latent heat rather than absent energy input.
Professional use. Document all thermal reservoirs, control surfaces and measurement periods. 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: Over a full cycle, ∮δQ=∮δW.
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 piston cycle receives net 250 kJ of heat and discharges 180 kJ as work in one stage; net work must equal 250 kJ over the entire cycle, including omitted work interactions.
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 one branch of a cycle to infer whole-cycle efficiency without summing the other branches.
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. Document all thermal reservoirs, control surfaces and measurement periods. 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 cycles, calorimetry and experimental balances. 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 Over a full cycle, ∮δQ=∮δW.
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 one branch of a cycle to infer whole-cycle efficiency without summing the other branches." 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 instrumented piston cylinder case that motivates this unit. The objective is to infer boundary work and heating from recorded p–V–T histories. 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 hysteresis, friction and small-scale heat leaks. 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.
A gas receives Q=120 kJ and expands doing W=35 kJ; its internal energy increases by 85 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.
For p=200 kPa constant and V rising by 0.030 m³, W_b=6.0 kJ done by the gas.
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 2 kg of an ideal gas with c_v=0.718 kJ/(kg K) heated 50 K, ΔU≈71.8 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.
For p1=200 kPa, V1=0.10 m³, V2=0.20 m³ and n=1.3, p2≈81.2 kPa and W≈12.5 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.
A piston cycle receives net 250 kJ of heat and discharges 180 kJ as work in one stage; net work must equal 250 kJ over the entire cycle, including omitted work interactions.
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.