SCIENCE · INVESTIGATE AND EXPLAIN

Correct a temperature record before comparing expansion

Temperature describes thermal state, not the amount of energy stored in an object. Two objects in thermal equilibrium have the same temperature; the zeroth-law relation allows a third system to serve as a thermometer. Equal temperature does not mean equal total internal energy, because mass, material and microscopic degrees of freedom can differ.

Learning outcome: Compare an offset-only fault, a gain-only fault and both together. Retain raw anchors and held-out correction, then predict which fault biases an expansion inferred from a temperature difference.

Starting recap

Declare temperature and time references, system boundaries and model regimes. Use absolute temperatures for ratios; distinguish state, path, oscillator phase and wave propagation.

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Try

If the same sensor has a=0.9 and b=−4, a 40 °C sample reads 32 °C; anchors −4 and 68 recover the same correct temperature. The physical expansion does not depend on the chosen readout convention.

Open the experiment

Predict

A constant additive Celsius sensor offset changes:

Your prediction and reason

Experiment

Compare an offset-only fault, a gain-only fault and both together. Retain raw anchors and held-out correction, then predict which fault biases an expansion inferred from a temperature difference.

Separate thermometer offset from scale and expansion

Worked teaching model · synthetic values · Synthetic indicated Celsius=a×true Celsius+b. Independently known anchors 0 and 80 °C; held-out true state 40 °C. A separate 1 m specimen has constant supplied linear expansion coefficient 2e-5/K from 20 to 60 °C. No physical heating.

Thermometer scale factor: 1.05 ratio Thermometer additive offset: 2 °C

Reset keeps your prediction, captures and practice history.

Disclosed thermometer response

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: affine response (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Disclosed thermometer response

affine response

true temperature (°C)	indicated temperature (°C)
0	2
1	3.05
2	4.1
3	5.15
4	6.2
5	7.25
6	8.3
7	9.35
8	10.4
9	11.45
10	12.5
11	13.55
12	14.6
13	15.65
14	16.7
15	17.75
16	18.8
17	19.85
18	20.9
19	21.95
20	23
21	24.05
22	25.1
23	26.15
24	27.2
25	28.25
26	29.3
27	30.35
28	31.4
29	32.45
30	33.5
31	34.55
32	35.6
33	36.65
34	37.7
35	38.75
36	39.8
37	40.85
38	41.9
39	42.95
40	44
41	45.05
42	46.1
43	47.15
44	48.2
45	49.25
46	50.3
47	51.35
48	52.4
49	53.45
50	54.5
51	55.55
52	56.6
53	57.65
54	58.7
55	59.75
56	60.8
57	61.85
58	62.9
59	63.95
60	65
61	66.05
62	67.1
63	68.15
64	69.2
65	70.25
66	71.3
67	72.35
68	73.4
69	74.45
70	75.5
71	76.55
72	77.6
73	78.65
74	79.7
75	80.75
76	81.8
77	82.85
78	83.9
79	84.95
80	86

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Indication at true zero Celsius	2	°C
Indication at true 80 Celsius	86	°C
Held-out indication at true 40 Celsius	44	°C
Corrected held-out temperature	40	°C
Held-out absolute temperature	313.15	K
Held-out Fahrenheit temperature	104	°F
Separate specimen expansion	0.0008	m

Two independent anchors remove an affine offset and gain, but do not prove a real sensor is affine.

Temperature differences have equal numerical size in kelvins and Celsius, while absolute ratios require kelvins. Thermal equilibrium is transitive in the zeroth-law idealization. Linear expansion Delta L=alpha L0 Delta T uses the physical temperature change, not an uncorrected reading. A cavity in a uniformly expanding solid also expands; it does not shrink because its boundary material expands inward.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

Two independent anchors remove an affine offset and gain, but do not prove a real sensor is affine.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Declare the state, system and observation

Build the algebraic model

The disclosed sensor reports indicated Celsius aT+b. Two independently known anchors at 0 and 80 °C identify offset and gain: subtract the low reading, then multiply by 80 divided by the anchor-reading difference. With a=1.05 and b=2, anchor readings are 2 and 86 °C, while a true 40 °C state reads 44 °C. Correcting gives (44−2)80/(86−2)=40 °C. A third record checks the assumed affine law but does not prove it for an unknown real instrument.

Check the original evidence packet

Absolute temperature in kelvins is Celsius plus 273.15. Thus 40 °C is 313.15 K, and Fahrenheit is 1.8×40+32=104 °F. A 40 °C temperature change is also a 40 K change, but an absolute ratio of Celsius values is not a thermodynamic temperature ratio. A gain error affects inferred changes; a constant offset cancels from a difference.

Challenge the domain and transfer

A separate 1 m specimen has supplied constant linear expansion coefficient 2×10⁻⁵/K. Warming it from 20 to 60 °C gives ΔL=αL0ΔT=0.0008 m. A uniformly heated hole expands with its surrounding material rather than shrinking. For isotropic small expansion, supplied volume coefficient is approximately 3α; a 1 L volume with this coefficient and a 40 K change grows about 2.4 mL. These are bounded linear models, not material strength or real heating instructions.

Worked original case

Bounded investigation

Compare an offset-only fault, a gain-only fault and both together. Retain raw anchors and held-out correction, then predict which fault biases an expansion inferred from a temperature difference.

Changed-case numerical practice

Try the changed case before feedback

A 2 m specimen has α=1.5×10⁻⁵/K and warms by 20 K in its stated linear range. Find expansion in millimetres.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and limits

Original content checked 30 October 2026 against OpenStax College Physics 2e. Packets are supplied or generated teaching evidence, not measured apparatus. No heating, pressure vessels, physical oscillators, sound exposure or construction is requested. Public checks and saved reports do not establish supervised practical skill, equipment safety or independent mastery.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why can equal temperatures coexist with very different total internal energies?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

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Previous: Check whether a fourth-power flow prediction remains admissible Next: Connect an ideal-gas state to a molecular energy distribution

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