# Learner lab record: Heat-engine boundary and efficiency ledger

Course: Thermodynamics and statistical reasoning

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

How do reservoir temperatures and uncounted transfers constrain the useful work of a cyclic engine?

## Setup

Use the heat-engine laboratory. Establish one complete hot-input, work-output, and cold-rejection ledger before changing either reservoir temperature.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Hot reservoir temperature | independent | K |
| Cold reservoir temperature | independent | K |
| Heat input | controlled | J |
| Work, rejected heat, and efficiency | dependent | J and % |

## Predict before changing controls

1. Predict the Carnot limit when both temperatures are equal.

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2. Predict how raising only the hot temperature changes the ideal limit.

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## Observation table

| Th | Tc | Qh | work | Qc | efficiency | Carnot limit |
| --- | --- | --- | --- | --- | --- | --- |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |

## Analyze

1. Does each run close Qh = W + Qc?

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2. Which run approaches the ideal bound most closely?

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3. Why is the Carnot value a ceiling rather than a promise?

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4. Which stored-energy change could mimic cycle output?

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## Evidence-bounded conclusion

For reservoirs at ___ K and ___ K, the engine delivered ___ J at ___% efficiency, compared with an ideal ceiling of ___%.

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