Specific Heat

Heat Capacity

joules per kelvin

Heat capacity says how many joules are needed for each kelvin of 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

Read heat capacity

A heat capacity of 10 joules per kelvin means each kelvin of warming needs 10 joules.

C=10 J/KC = 10\ \text{J/K}
Heat capacity caseThe temperature change and heat bar are computed together.30 Jheat300 Kstart303 Kend

Multiply by the temperature change

For a 3 kelvin change, use 3 copies of that energy.

Q=CΔTQ = C\Delta T

Compute the heat

The transferred heat is 10 times 3, or 30 joules.

Q=10 J/K⋅3 K=30 JQ = 10\ \text{J/K}\cdot 3\ \text{K} = 30\ \text{J}
Heat capacity caseThe temperature change and heat bar are computed together.30 Jheat300 Kstart303 Kend

Capacity scales the heat directly

Hold the temperature change at 3 kelvin. The diagram shows the middle row; more joules per kelvin means more total heat.

CΔTQ5 J/K3 K15 J10 J/K3 K30 J15 J/K3 K45 J\begin{array}{c|c|c}C&\Delta T&Q\\5\ \text{J/K}&3\ \text{K}&15\ \text{J}\\10\ \text{J/K}&3\ \text{K}&30\ \text{J}\\15\ \text{J/K}&3\ \text{K}&45\ \text{J}\\\end{array}
Heat capacity caseThe middle table row is the checked diagram.30 Jheat300 Kstart303 Kend

Temperature change also scales heat directly

Now hold the heat capacity at 10 joules per kelvin. More kelvin of warming needs more joules.

CΔTQ10 J/K1 K10 J10 J/K3 K30 J10 J/K5 K50 J\begin{array}{c|c|c}C&\Delta T&Q\\10\ \text{J/K}&1\ \text{K}&10\ \text{J}\\10\ \text{J/K}&3\ \text{K}&30\ \text{J}\\10\ \text{J/K}&5\ \text{K}&50\ \text{J}\\\end{array}
Heat capacity caseThe middle table row is the checked diagram.30 Jheat300 Kstart303 Kend