Temperature and Heat — Question 5

Question 5

A contact feels colder because it transfers energy faster

A simplified contact model takes skin at 305 K and a surface at 295 K, both maintained at those temperatures. The heat-transfer rate is $P=G(T_{\mathrm{skin}}-T_{\mathrm{surface}})$. Material M has $G_M=4.0\,\mathrm{W/K}$; material W has $G_W=.25\,\mathrm{W/K}$. Contact lasts 2.0 s.

1. Find the outward skin heat for each material and their ratio.

2. If both surfaces are instead at 310 K, find the signed heat into the skin over 2.0 s. What can a stronger thermal sensation establish about temperature?

Question 5 - Solution

A contact feels colder because it transfers energy faster

(a) Method and calculation

$$P_M=4(10)=40\,\mathrm W,\quad P_W=.25(10)=2.5\,\mathrm W.$$$$Q_{M,\mathrm{out}}=80\,\mathrm J,\quad Q_{W,\mathrm{out}}=5.0\,\mathrm J,\quad Q_M/Q_W=16.$$

(b) Interpretation and further calculation

$$Q_{\mathrm{skin}}=G(T_{\mathrm{surface}}-T_{\mathrm{skin}})\Delta t.$$$$Q_{M,\mathrm{skin}}=40\,\mathrm J,\quad Q_{W,\mathrm{skin}}=2.5\,\mathrm J.$$The direction reverses for a hotter surface. Magnitude also depends on conductance, so stronger sensation alone is not a temperature ranking.

Physical check

This maintained-temperature model neglects contact cooling and biological response; it isolates the transfer-rate distinction.