Why Metal Objects Feel Colder Than Wood Ones?
Thermal conductivity is only one reason why metal surfaces feel colder than wood surfaces. There is another equally important effect at play, which Cecil omits to mention. Wood has
a very low heat capacity compared to metal objects.
When you touch an object that is at room temperature, heat flows from your hand to the object,
which warms the object's surface. This is a transient heat transfer problem. Transient conduction
heat transfer depends on BOTH heat capacity and conductivity. Heat Capacity is the product of density times specific heat.
The instantaneous heat transfer from your hand depends upon capacity of the object to absorb heat, as well as the object's thermal conductivity. If you were to touch two surfaces with the same conductivity, the object with the higher heat capacity (density x specific heat) would feel
colder. Heat would flow at a greater rate from your hand into the surface.
The proof is simple. Think about plunging your hand into a sink of water that is at room temperature. It feels very cold. Water has a high heat capacity, but relatively low thermal conductivity (about 250 times lower than aluminum).
In fact, analysis (lots of calculus) shows that instantaneous heat flux (and hence, the intensity of the cold sensation) is roughly proportional to square root of heat capacity. In comparison, the
instantaneous heat flow also depends upon the square root conductivity.
So, heat capacity has just as much effect as the thermal conductivity on the sensation of cold you
feel when you touch a metal surface.
Heat Transfer Guy
Well, yes and no, Heat Transfer Guy. Some numbers would help to compare magnitudes of these properties. From my Mark's Standard Handbook for Mechanical Engineers and Mechanical Engineer's Reference Manual:
density = 2732 kg/m3
specific heat = 0.481 kJ/(kg*K)
heat capacity = 1314 kJ/(m3*K)
thermal conductivity = 117 Btu/(hr*ft*F)
density = 7900 kg/m3
specific heat = .216 kJ/(kg*K)
heat capacity = 1706 kJ/(m3*K)
thermal conductivity = 36 Btu/(hr*ft*F)
density = 400-700 kg/m3
specific heat = 2.4 - 2.8 kJ/(kg*K)
heat capacity = 1120 - 1680 kJ/(m3*K)
thermal conductivity = 0.06-0.20 Btu/(hr*ft*F)
density = 1000 kg/m3
specific heat = 4.177 kJ/(kg*K)
heat capacity = 4177 kJ/(m3*K)
thermal conductivity = 0.319 Btu/(hr*ft*F)
(sorry about mixing units)
Now, as Cecil said, the thermal conductivity of metals (aluminum and iron, in the examples above) is much greater than that of wood: the difference is about three orders of magnitude. The heat capacity for metals and woods, however, is basically the same. That doesn't make what you said wrong, because the heat capacity of a material is extremely important in how cold it will feel. It's just that, in comparing wood and metal, the heat capacity is not all that much different.
Additionally, I think your analogy using a sink full of water is flawed. Water does have a high heat capacity and relatively low thermal conductivity; however, the numbers are not hugely different from wood. What you're overlooking is that, in water, heat can convect away from your hand, so that the actual "heat removal rate" is much larger than the thermal conductivity would imply.