Mass Factor Scan - Heat & Thermodynamics Step by Step

A three-point scan makes the direct mass-to-heat relationship visible before the formula is compressed. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Hold material and warming fixed

Use one material with specific heat 5 joules per kilogram per kelvin, and warm every sample by 4 kelvin.

Q = mc\Delta T

First mass point

The first sample has the smallest mass, so it gets the first row in the scan.

Q_{\text{first}} = 1\ \text{kg}\cdot 5\ \text{J/(kg K)}\cdot 4\ \text{K} = 20\ \text{J}

Second mass point

The same material and same warming now act on a larger mass. Only the mass changed.

Q_{\text{second}} = 2\ \text{kg}\cdot 5\ \text{J/(kg K)}\cdot 4\ \text{K} = 40\ \text{J}

Third mass point

The third mass makes the direct pattern visible without needing to infer it from two cases.

Q_{\text{third}} = 3\ \text{kg}\cdot 5\ \text{J/(kg K)}\cdot 4\ \text{K} = 60\ \text{J}

Read the three-point mass scan

With material and warming fixed, mass and heat rise together. The diagram and the table use the same three checked values.

\begin{array}{c|c|c|c}m&c&\Delta T&Q\\1\ \text{kg}&5\ \text{J/(kg K)}&4\ \text{K}&20\ \text{J}\\2\ \text{kg}&5\ \text{J/(kg K)}&4\ \text{K}&40\ \text{J}\\3\ \text{kg}&5\ \text{J/(kg K)}&4\ \text{K}&60\ \text{J}\\\end{array}