This might be a very elementary question. Considering that electrons in typical metals have very high Fermi velocity, why is it that when you touch a metal you feel cold? My intuition tells me that due to Fermi-Dirac distribution only a tiny fraction of electrons near the Fermi surface participate in heat conduction. Heat transfer due to electrons is tiny compared to transfer due to phonons. Is this reasoning correct?
[Physics] why do metals feel cold when electron moves at Fermi velocity
electronsquantum mechanicsthermodynamics
Related Solutions
Yes, the deodorant contains a mixture of low boiling point alkanes, such as butane, that form a liquid under pressure but evaporate when the pressure falls to one atmosphere as they leave the can. It's primarily the latent heat of vaporisation that reduces the temperature and makes it feel cold.
In addition to this, deodorants (as opposed to antiperspirants) contain ethanol - they are essentially just a solution of perfume in ethanol plus propellant. The ethanol evaporates on the skin and again the latent heat of vaporisation cools the skin.
In a can of deodorant the dip tube goes down into the liquid propellant. When you press the button the pressure in the can forces liquid alkane up the dip tube and out. The alkane mostly evaporates in the tube and nozzle, but if you hold the can very close to your skin you can get liquid alkane on the skin. This evaporates very rapidly, and it's really cold!
Short answer:
The thermometer measures actual temperature (which is the same for both), while your hand measures the transfer of energy (heat), which is higher for the pot than the air.
Long answer:
Keyword: Thermal Conductivity
The difference is a material-specific parameter called thermal conductivity. If you are in contact with some material (gas, liquid, solid), heat, which is a form of energy, will flow from the medium with higher temperature to the one with low temperature. The rate at which this happens is determined by a parameter called thermal conductivity. Metals are typically good heat conductors, which is why metal appears colder than air, even though the temperature is the same.
Regarding your second question: the thermometer will show the same temperature. The only difference is the time at which thermal equilibrium is achieved, i.e. when the thermometer shows the correct temperature.
Final remark: the rate at which heat (energy) is drained from your body determines whether you perceive a material as cold or not, even if the temperature is the same.
For reference, here is a table which lists thermal conductivities for several materials:
Best Answer
In a Fermi-Dirac distribution, the relationship between temperature and the speed of particles is not intuitive. Even at cold temperatures, fermions can have high speeds simply because of degeneracy - the lower momentum states "fill up", leaving only states with large momentum available, and this is true even at very cold temperatures. However, the heat capacity of the conduction electrons is negligible - heat cannot be extracted precisely because there are no lower energy states available.
The reason that metals feel cold is because they have a high thermal conductivity. This can also be attributed to degeneracy of the conduction electrons, since in a degenerate electron gas there are few available lower momentum slots into which a conduction electron can be scattered. This means that the electrons have a relatively long mean free path between scattering events and are able to transfer heat efficiently from your finger into the metal and then away. Thus the temperature of the metal where you touch it does not rise to match your skin temperature.
I don't think phonons come into this at all. In metals, electron heat conduction dominates phonon transport.