# Heat-budget lab · complete paper and tactile equivalent

The [offline interactive](heat-budget-lab.html) changes **one factor** in the invented `Q=mcΔT` model. This page contains the same method, exact cases, prediction comparison and limits. No device, account, purchase, heat source or real material sample is needed.

**Paper method:** (1) Write the fictional mass `m` in kg, stipulated specific heat capacity `c` in J kg⁻¹ K⁻¹ and positive temperature rise `ΔT` in K. (2) Predict `Q` in J before multiplying. (3) Calculate `Q=m×c×ΔT`; cancel kg and K to leave J. (4) Change exactly one of `m`, `c` or `ΔT`, keeping the other two fixed. Predict the new Q and calculate it. (5) Compare your prediction with the calculation by taking the absolute difference in J. (6) Say that the proportional change holds only in this single-phase, constant-c, no-loss model. A real heater or touch-safety result is not established.

| Case | Original calculation | One-factor change | New calculation | Useful explanation |
| --- | --- | --- | --- | --- |
| A | `0.50 kg × 2,000 J kg⁻¹ K⁻¹ × 4 K = 4,000 J` | Double mass to `1.00 kg` | `1.00 × 2,000 × 4 = 8,000 J` | With c and ΔT fixed, Q doubles. A prediction of 8,000 J differs by 0 J. |
| B | `0.50 kg × 1,000 J kg⁻¹ K⁻¹ × 6 K = 3,000 J` | Halve rise to `3 K` | `0.50 × 1,000 × 3 = 1,500 J` | With m and c fixed, Q halves. A prediction of 1,500 J differs by 0 J. |

**Tactile route:** Put MASS, SPECIFIC HEAT CAPACITY and TEMPERATURE CHANGE cards in three labelled sleeves with units. Assemble a left-to-right multiplication chain ending in an ENERGY J card. Put a PREDICTION card aside before turning over any answer card. Replace **one** factor card only, and use a second ENERGY J card for the calculated output. A learner can direct a supporter to move pieces. Texture alone is insufficient: keep Braille, large-text or spoken labels.

**Optional third paper case:** Keep `m=0.50 kg` and `ΔT=4 K` while doubling the invented c from `2,000` to `4,000 J kg⁻¹ K⁻¹`: Q changes from `4,000` to `8,000 J`. This is a stipulated mathematical what-if, not a real material claim.

**Original resource rights:** © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit author, source, licence and changes. Inline interactive code is Apache-2.0.