Energy Foundations, Enthalpy and First Law Balances

Central engineering problem

Energy must be counted across a chosen boundary using one sign convention and consistent enthalpy reference states.

The unit develops four tightly connected ideas. A process description should become a quantitative and testable claim: an explicit boundary, evidence for values, dimensional consistency, and a way to distinguish real physical behavior from model simplifications. The relevant measurements and operating envelopes must be named before making a process decision. In introductory chemical engineering, a plausible numerical result is necessary but not sufficient; it must also obey conservation, physical feasibility and operational safety.

Learning outcomes

After studying this unit, a student should be able to explain the physical role of the four topics, construct or interpret a simple numerical representation, identify a falsifying measurement, and document how the assumptions restrict the result. Numerical work should use explicit material or energy bases and show uncertainty or sensitivity whenever decisions depend on approximate data.

Lesson sequence

• [Heat, work and energy inventories](../lessons/unit-05-lesson-01.html)
• [Heat capacity and sensible heating](../lessons/unit-05-lesson-02.html)
• [Phase change and enthalpy references](../lessons/unit-05-lesson-03.html)
• [Heat exchangers and energy auditing](../lessons/unit-05-lesson-04.html)

Interactive laboratories

• [Lab 09: Sensible heat duty](../labs/lab-09.html)
• [Lab 10: Countercurrent heat-exchanger driving force](../labs/lab-10.html)

Synthesis activity

Build a one-page process evidence sheet that distinguishes four columns: directly observed quantities, derived quantities, estimated properties, and external constraints. For each lesson's primary equation, test whether a 10% change in its dominant input yields a proportionate response. Explain exceptions, including compositions bounded between zero and one and physical states requiring feasibility checks. Conclude with at least two measurements needed to confirm the result in a real laboratory or plant.

Assessment standard

Successful work must show a system boundary or process purpose, symbolic equations before values, units during substitution, an independent conservation or limiting-case check, and a concise explanation of where a more advanced treatment is required. Attach plots only when their input assumptions are documented. The purpose is transferable engineering reasoning rather than memorized formula application.

Unit 5.1: Heat, work and energy inventories

Chemical Engineering Fundamentals · Unit 5: Energy foundations

Purpose and measurable learning outcomes

Heat is energy crossing the boundary because of temperature difference; shaft and electrical work cross through other interactions. The first-law statement depends on the chosen control volume and reference convention. Open systems transport enthalpy with mass, while closed systems change internal energy. Distinguish rate in kW from integrated energy in kWh or MJ.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

Check sign convention in open and closed energy balances. For a steady open heater with negligible shaft work and insignificant velocity changes, the hot-side duty should match the enthalpy rise of the cold side plus losses. Energy transported by mass is not typically the same as heat crossing the equipment boundary. A 90 kW heater adds 90 kJ every second, whereas 90 kWh is a quantity of integrated energy. A reliable report labels both and provides the chosen time basis. Energy can be conserved even when available useful work is degraded by irreversibility.

Governing quantitative relationship

If heater input is 90 kW for 2 h, supplied energy is 180 kWh = 648 MJ.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A well-insulated stirred tank is heated electrically with known power. Explain where electrical energy appears if temperature rises and a portion vaporizes.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Equating heat and temperature or treating a constant power input as a fixed quantity of energy.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A well-insulated stirred tank is heated electrically with known power. Explain where electrical energy appears if temperature rises and a portion vaporizes. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Equating heat and temperature or treating a constant power input as a fixed quantity of energy. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 09](../labs/lab-09.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-05.html) · [Book contents](../index.html)

Unit 5.2: Heat capacity and sensible heating

Chemical Engineering Fundamentals · Unit 5: Energy foundations

Purpose and measurable learning outcomes

Specific heat links sensible heat change with temperature over a stated range. Constant Cp is a convenient approximation; for wider temperature spans integrate Cp(T). For a fluid changing phase, separate heating sensible portions and phase-change enthalpy. A process heat duty calculated from temperatures alone is meaningless without flow and properties.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

For a single-phase liquid stream with approximately constant heat capacity, the heating duty scales with flowrate and temperature rise. If the mass rate doubles while inlet and outlet temperatures remain fixed, ideal duty doubles. But pump heat, viscosity changes, mixing and heat losses can introduce departures. When heat capacity varies strongly, approximate the integral numerically or use a verified property method rather than stretching a constant value. A sensitivity graph should therefore distinguish the assumed property model from observed plant behavior and should include ranges in which phase change is absent.

Governing quantitative relationship

Qdot = mdot Cp ΔT; 2 kg/s × 4.2 kJ/(kg·K) × 15 K = 126 kW.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A water stream at 1.5 kg/s warms from 20°C to 60°C. Compute ideal duty and discuss a possible correction for heat losses.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Applying a single gas heat capacity to an unknown multiphase or reacting mixture.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A water stream at 1.5 kg/s warms from 20°C to 60°C. Compute ideal duty and discuss a possible correction for heat losses. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Applying a single gas heat capacity to an unknown multiphase or reacting mixture. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 10](../labs/lab-10.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-05.html) · [Book contents](../index.html)

Unit 5.3: Phase change and enthalpy references

Chemical Engineering Fundamentals · Unit 5: Energy foundations

Purpose and measurable learning outcomes

Latent heat represents energy associated with phase change at a specified pressure. Reference enthalpy levels are arbitrary but differences must use consistent baselines and phases. In a boiling process, efficiency also depends on sensible preheating, vapor quality and losses. Watch for condensation, flashing and temperature glide in mixtures.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

A heater feeding a vaporizer may need both sensible and latent energy. For a water-like example with 200 kg/h feed, Cp≈4.2 kJ/(kg·K), inlet 25°C, boiling 100°C, and vaporized fraction 0.25, sensible heating is 200×4.2×75=63,000 kJ/h. At illustrative latent heat 2250 kJ/kg, vaporization adds 0.25×200×2250=112,500 kJ/h. Total ideal duty is 175,500 kJ/h≈48.75 kW. A real balance must handle pressure-dependent properties, actual vapor fraction, heat loss and other streams.

Governing quantitative relationship

For 2 kg water vaporized using illustrative h_fg = 2250 kJ/kg, latent duty is 4500 kJ before preheating or losses.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A 200 kg/h stream warms from 25°C to 100°C and 25% evaporates. Form a two-part energy balance and identify needed property data.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Treating an entire liquid stream as vaporized because its bulk temperature reaches nominal boiling point.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A 200 kg/h stream warms from 25°C to 100°C and 25% evaporates. Form a two-part energy balance and identify needed property data. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Treating an entire liquid stream as vaporized because its bulk temperature reaches nominal boiling point. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 09](../labs/lab-09.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-05.html) · [Book contents](../index.html)

Unit 5.4: Heat exchangers and energy auditing

Chemical Engineering Fundamentals · Unit 5: Energy foundations

Purpose and measurable learning outcomes

A heat exchanger transfers heat between fluid streams and is limited by energy conservation, temperature driving force, heat-transfer area and fouling. Countercurrent and cocurrent arrangements have different terminal differences. LMTD is not the arithmetic mean except in a limiting case; when terminal differences approach equality, use the continuous limit. Compare inferred duties on both sides and report imbalance.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

In a countercurrent exchanger, terminal differences are ΔT1=T_h,in−T_c,out and ΔT2=T_h,out−T_c,in. For hot 90→65°C and cold 20→50°C, the terminal differences are 40 and 45 K. Their log-mean is (40−45)/ln(40/45)≈42.45 K. If one difference becomes zero or negative, the basic positive-driving-force model is infeasible. A positive LMTD still does not specify area without an overall heat-transfer coefficient and required heat duty. An energy balance on both streams is a separate necessary check.

Governing quantitative relationship

For a stream with mdot=1 kg/s, Cp=4 kJ/(kg K) and ΔT=20 K, Qdot=80 kW.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

An exchanger heats cold water from 20 to 50°C using hot water from 90 to 65°C. Compute terminal differences for counterflow and discuss feasibility.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Using an outlet temperature that exceeds the hot inlet temperature without a heat pump or additional energy input.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. An exchanger heats cold water from 20 to 50°C using hot water from 90 to 65°C. Compute terminal differences for counterflow and discuss feasibility. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Using an outlet temperature that exceeds the hot inlet temperature without a heat pump or additional energy input. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 10](../labs/lab-10.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-05.html) · [Book contents](../index.html)

Unit 5 applied engineering project — A heat-recovery demonstration system

Setting and purpose

A warm process stream transfers energy to a colder process stream; a heater provides trim energy. This is a synthetic teaching case, not a recommendation to operate a real process. Students must select reasonable illustrative numbers, label every invented number as an assumption, and keep all units, reference conditions and composition bases visible. The purpose is to assemble the unit's concepts into a consistent model that a reviewer can challenge.

Engineering question

Calculate the sensible heat changes, inspect terminal temperature feasibility and construct an energy audit with a clearly declared time basis. State a single primary decision being supported, such as selecting a material-balance boundary, accepting a measurement, identifying a missing outlet or prioritizing an additional experiment. Do not use an unsupported plant-wide profit number or an unverified regulatory threshold to justify the decision.

Required evidence and calculation plan

1. Write a process statement that defines input materials, expected outputs and the relevant boundaries. Distinguish a batch inventory from a flow and give the measurement time basis.
2. Build an input data table with dimensions, source type, uncertainty estimate and acceptable bounds. Separate readings from engineering assumptions.
3. Derive at least three equations rather than relying only on a calculator. For each, show a dimensional check and a feasible limiting case. Include a separate component balance when a concentration or reaction is involved.
4. Carry out two contrasting cases: a nominal baseline and a plausible changed operating condition. If the changed condition violates the simplified model, stop and write that result as an important finding.
5. Use the unit laboratories as computational demonstrations; export plots, retain input settings, and compare with a direct hand calculation. Plots are evidence about a mathematical model, not proof about an operating plant.
6. Describe data or safety limitations. Include possible missing streams, property correlations, instrument bias, parameter dependence and common-cause uncertainty where they matter.
7. Communicate the result as a reproducible engineering note with an executive statement, flow diagram, equations, tables, a source list and an open list of unresolved questions.

Review checkpoints

• Conservation: material and energy accounting closure must be explicit; an unresolved residual is named, not silently forced to zero.
• Feasibility: compositions must be physically bounded and equipment temperatures and pressures checked against the model's assumptions.
• Traceability: a competent reader can identify exactly which values are assumed, measured or derived, and can reproduce the major quantities.
• Safety and ethics: no classroom calculation is presented as industrial relief sizing, pharmaceutical validation, field authorization or environmental compliance proof.

Deliverables

Submit one concise process diagram, one independently checkable calculation sheet, two simulation exports, a one-page uncertainty/sensitivity commentary and a 250-word statement on what evidence would change your conclusion. Defend the chosen model scope and openly identify a more advanced analysis needed before industrial deployment.

Unit 5 assessment: Energy foundations

These 12 problems combine quantitative reproduction, model validity, and audit methodology. Answers below are intended as diagnostic reasoning, not fabricated plant data.

Question 1: analysis of heat, work and energy inventories

A well-insulated stirred tank is heated electrically with known power. Explain where electrical energy appears if temperature rises and a portion vaporizes.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 5.1. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 2: model validity

Equating heat and temperature or treating a constant power input as a fixed quantity of energy. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 3: quantitative audit

Use the lesson's worked equation: If heater input is 90 kW for 2 h, supplied energy is 180 kWh = 648 MJ. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 5: analysis of heat capacity and sensible heating

A water stream at 1.5 kg/s warms from 20°C to 60°C. Compute ideal duty and discuss a possible correction for heat losses.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 5.2. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 6: model validity

Applying a single gas heat capacity to an unknown multiphase or reacting mixture. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 7: quantitative audit

Use the lesson's worked equation: Qdot = mdot Cp ΔT; 2 kg/s × 4.2 kJ/(kg·K) × 15 K = 126 kW. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 9: analysis of phase change and enthalpy references

A 200 kg/h stream warms from 25°C to 100°C and 25% evaporates. Form a two-part energy balance and identify needed property data.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 5.3. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 10: model validity

Treating an entire liquid stream as vaporized because its bulk temperature reaches nominal boiling point. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 11: quantitative audit

Use the lesson's worked equation: For 2 kg water vaporized using illustrative h_fg = 2250 kJ/kg, latent duty is 4500 kJ before preheating or losses. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 13: analysis of heat exchangers and energy auditing

An exchanger heats cold water from 20 to 50°C using hot water from 90 to 65°C. Compute terminal differences for counterflow and discuss feasibility.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 5.4. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 14: model validity

Using an outlet temperature that exceeds the hot inlet temperature without a heat pump or additional energy input. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 15: quantitative audit

Use the lesson's worked equation: For a stream with mdot=1 kg/s, Cp=4 kJ/(kg K) and ΔT=20 K, Qdot=80 kW. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.