A thermal program needs both heat capacity and temperature-step factor scans before the total heat budget is trusted. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Ramp heat has two factors

The ramp helper computes each heat bar as heat capacity times temperature change. This scan changes those factors separately before summing the program.

Qi=CΔTiQ_i=C\Delta T_i
Ramp sequenceEach programmed ramp has checked heat energy.12 Jramp20 Jramp16 Jramp48 Jtotalramp program

Capacity and delta lists give different row shapes

The middle row keeps the same delta list as the first row but changes capacity. The last row changes the delta distribution, so the bars become equal before they sum.

CΔT listQ listQtotal2 J/K3 K,5 K,4 K6 J,10 J,8 J24 J4 J/K3 K,5 K,4 K12 J,20 J,16 J48 J3 J/K4 K,4 K,4 K12 J,12 J,12 J36 J\begin{array}{c|c|c|c}C&\Delta T\text{ list}&Q\text{ list}&Q_{\text{total}}\\2\ \text{J/K}&3\ \text{K},5\ \text{K},4\ \text{K}&6\ \text{J},10\ \text{J},8\ \text{J}&24\ \text{J}\\4\ \text{J/K}&3\ \text{K},5\ \text{K},4\ \text{K}&12\ \text{J},20\ \text{J},16\ \text{J}&48\ \text{J}\\3\ \text{J/K}&4\ \text{K},4\ \text{K},4\ \text{K}&12\ \text{J},12\ \text{J},12\ \text{J}&36\ \text{J}\\\end{array}
Ramp sequenceEach programmed ramp has checked heat energy.12 Jramp12 Jramp12 Jramp36 Jtotalramp program

The final row closes from equal bars

The final row has three equal checked heat bars. Their sum is the program heat budget; it is not a separate estimate.

12 J+12 J+12 J=36 J12\ \text{J}+12\ \text{J}+12\ \text{J}=36\ \text{J}
Ramp sequenceEach programmed ramp has checked heat energy.12 Jramp12 Jramp12 Jramp36 Jtotalramp program