Conventionally, though with justifications, space is said to begin at the Kármán line which is
100km from Earth surface, i.e., still pretty close. The atmospheric
pressure at this altitude drops to about 0.032 Pa (wikipedia), which is still a
lot more than outer space (less than $10^{-4}$ Pa according to wikipedia)
The phase diagram of water shows that, at this pressure level, water
can exist only as a solid or as vapor, depending on temperature, but
not as a liquid. The phase transition between solid and gaz at that
low pressure takes place near 200°K (around -73°C), which is not that cold.
So, if you drop in space a blob of water at room temperature and
pressure it will instanly start to evaporate (boil) and decompress.
Here I am not sure about what happens. There are accounts from
astronauts on the web that explain that the water (actually urine)
will first vaporise then desublimate into tiny crystals. But no
explanation of the actual physical phenomena that drive it.
My own reconstruction of what could happen (before I saw these sites)
is the following.
First the loss of pressure propagates very fast in the liquid (speed of
sound?) while loss of temperature (heat) propagates slowly (as all beer lovers
know from their fridge). So the boiling will essentially take place
uniformly in the whole liquid. Phase transition from liquid to gas
absorbs heat, and that is what will cool the water very quickly, as
it evaporates.
My guess is also that the energy loss will cool the water down to
sublimation temperature (solid-gas transition) before it all
evaporates, so that some parts of the liquid may be cooled down to
freezing before they have time to evaporate. But as boiling takes
place everywhere, it actually breaks the remaining water into tiny
fragments that cristallize, and possibly also collect some of the
vapor to grow.
Anyway, you apparently get snow.
But the cooling is due to evaporation, which is very fast,
much more than to radiation which has hardly any time to take place.
Numerical evaluation
We analyze what becomes of available heat to understand whether some water freezes directly. This is a very rough approximation as the figures used are
actually somewhat variable with temperature, but I cannot find the
actual values for the extreme temperature and pressures being
considered.
The specific latent heat of evaporation of water is 2270 kJ/kg. The
specific heat of water is 4.2 kJ/kgK Hence, evaporating 1 gram of
water can cool 2270/4.2 = 540 grams of water by 1°K, or 5.4 grams by
100°K which is about the difference between room temperature and water
(de)sublimation temperature in space. So my hypothesis that there is
not enough heat available to vaporize all the water is correct, as
only about one sixth of the water can be vaporized with the available
heat.
Out of 5.4g of water, 1g will evaporate, though may cool down to just
above the sublimation temperature of 200°K, while the remaining 4.4g
will be cooled to sublimation temperature without vaporizing,
yet. The remaining 4.4g cannot remain liquid, hence, one part freezes,
thus freeing some latent het for the other part to vaporize. The ratio
between the two part is inversely proportional to the specific latent
heat for freezing and vaporizing.
Latent heat for freezing is 334 kJ/kg.
The sum of both latent heat is 2270+334=2604 kJ/kg. These figure are
very approximate. As a sanity check, the latent heat of sublimation of
water is approximately 2850kJ/kg (wikipedia), which show that the
figures are probably correct within a 10% approximation.
The ratio divides the remaining 4.4g into approximately 3.8g that
freezes and 0.6g that evaporates, making it a total of 1.6g of
vaporized water.
So, skipping a quick calculation, we find that about 70% of the water freezes into some kind of snow, while the remaining 30% are vaporized. And it all happens rather quickly.
I was actually uneasy about this account of astronauts stories of
water boiling and then desublimating at once, because that would leave
us with all the heat to get rid of very quickly. How? Does anyone have a better
account?
A last remark is that there always will be some part of the water that
gets frozen. I thought initially that very hot water might provide enough heat to vaporize itself completely un low pressure. The critical point of liquid water is at 650°K (with a much higher pressure than you care to create in space: 22MPa), which is
only 450° above the sublimation temperature. But the water should be
cooled by 540° to provide enough heat to evaporate completely. So
the water temperature will drop to the sublimation threshold before
enough heat can be supplied to evaporate it completely. This problably
a very simplistic analysis, though. I leave the rest to specialists.
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
I think you are speaking of a clinical thermometer which records the maximum temperature it reaches. The thermometer has a narrow kink in the bore near the bulb that causes the mercury thread to break at that point when the volume of mercury in the bulb shrinks (the image you've posted actually shows that). As a consequence the top of the thread does not retract from the high-point reading. (One might worry about the mercury above that break-point shrinking, but there is very little mercury in the thread, most of it is in the bulb. Consequently there is little effect from the volume of the thin thread getting smaller.)
The reason that the thermometer is designed this way is so that the doctor or nurse can take their time in reading the thermometer --- which would otherwise begin to read lower temperatures as soon at it is removed from the patients mouth, or wherever.
Shaking the thermometer after it has coooled to room temperature causes the mercury in the broken thread to reconnect with the mercury in the bulb, and allow it to be used again.