Mass and Temperature Contrast - Heat & Thermodynamics Step by Step

For a fixed material, heat is directly proportional to both mass and temperature change. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start from the base case

The base case needs 30 joules of heat.

Q_{\text{base}} = 30\ \text{J}

Double the mass

Keeping the material and warming the same, doubling mass doubles the heat to 60 joules.

Q_{\text{more mass}} = 2\cdot 30\ \text{J} = 60\ \text{J}

Double the temperature change

Keeping the mass and material the same, doubling the temperature change also gives 60 joules.

Q_{\text{more warming}} = 2\cdot 30\ \text{J} = 60\ \text{J}

Either doubled factor doubles the heat

The bars show three comparable cases on one scale. Mass and temperature change are separate factors, but each is direct.

\begin{array}{c|c|c}\text{case}&\text{changed factor}&Q\\\text{base}&\text{none}&30\ \text{J}\\\text{more mass}&m&60\ \text{J}\\\text{more warming}&\Delta T&60\ \text{J}\end{array}