Metal and wood to the touch

Problem

Placing a hand on a metal block at $20\;^\circ\text{C}$ it feels “cold”; placing it on a book, also at $20\;^\circ\text{C}$, it feels “less cold”. Explain the phenomenon, carefully distinguishing temperature from rate of heat transfer.

Solution

Same temperature. Both objects are in equilibrium with the same room, so they have exactly the same temperature $20\;^\circ\text{C}$. The perceived difference therefore cannot depend on temperature.

Different conductivity. Metal has a much higher thermal conductivity than wood (or paper). When the hand — warmer, at $\sim 35\;^\circ\text{C}$ — touches the metal, it draws heat from the skin much faster, cooling it quickly. Wood, a poor conductor, draws heat away slowly and the skin stays close to its own temperature.

What we perceive. The sensation of “cold” is generated by the skin’s receptors and depends on the rate at which heat leaves the hand, not on the temperature of the object touched. Same temperature, different heat flows → different sensations.

$\ev{\text{Same } T,\ \text{different conductivity}}$

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Topics: Thermodynamics Concepts: Heat transfer · Temperature