Ramp Sequence Energy Scan - Biophysical Instrumentation III: Control, Detectors, and Throughput Step by Step

A thermal program closes when every ramp energy and the total cite the same heat bars. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Each ramp multiplies heat capacity by temperature change

The rendered program uses heat capacity 4 J/K. Its first ramp changes by 5 K and uses 20 J.

Q=C\Delta T=4\ \text{J/K}\cdot5\ \text{K}=20\ \text{J}

Three ramp programs show energy addition

Every row lists the programmed temperature changes, the computed ramp heats, and the total energy. The total is a sum of checked bars, not a separate estimate.

\begin{array}{c|c|c|c}C&\Delta T\text{ list}&Q\text{ list}&Q_{\text{total}}\\4\ \text{J/K}&5\ \text{K},7\ \text{K},8\ \text{K}&20\ \text{J},28\ \text{J},32\ \text{J}&80\ \text{J}\\2\ \text{J/K}&4\ \text{K},6\ \text{K},10\ \text{K},10\ \text{K}&8\ \text{J},12\ \text{J},20\ \text{J},20\ \text{J}&60\ \text{J}\\6\ \text{J/K}&1\ \text{K},4\ \text{K},2\ \text{K}&6\ \text{J},24\ \text{J},12\ \text{J}&42\ \text{J}\\\end{array}

The total closes from the listed ramp heats

For the small program, the checked ramp heats add to 42 J.

6\ \text{J}+24\ \text{J}+12\ \text{J}=42\ \text{J}