Why do we "feel" steam at 100 °C as hotter than water at 100 °C? A block of ice as big as a room will have more thermal energy than a cup of hot tea.
But the tea feels hotter because the average kinetic energy (temperature) is higher in case of tea.
I conclude from this that total energy doesn't matter when it comes to what feels hotter.
But it is said that steam at 100 °C feels hotter than water at 100 °C because steam has more energy, which is contradictory to my conclusion.
Please explain where have I gone wrong.
To resolve the confusions: When we heat water, its temperature keep on increasing. Boiling starts when it reaches 100 degree Celsius and bulk vaporization takes place. These vaporised molecules, possessing same energy of water (is at same temperature as it) plus latent heat of vaporisation, is what I am referring to as steam. So, it has more energy but same temperature.
I expected no confusion regarding such steam causing more severe effects. But now that it has, let me mention that this is a common secondary textbook fact, that is taught and studied in India. Here is a link to a related school material: https://byjus.com/questions/what-produces-more-severe-burns-boiling-water-or-steam/.
 A: Based on some heat transfer experience, these effects can be quantified fairly easily if we neglect convective heat transfer in the water and steam, and assume that the thermal properties of flesh are about the same as those of liquid water.  In that case, if the liquid water at 100 C is suddenly brought into contact with flesh at 37 C, the interface temperature will change, and attain he average value of (100 + 37)/2 = 68.5 C.  Pretty hot.
Now for the case of steam at 100 C suddenly brought in contact with flesh at 37 C.  In this case, a layer of condensed liquid water will begin to form on the surface of the flesh, and the thickness of this condensed layer $\delta(t)$ will increase as time progresses.  The rate heat release from condensation (per unit area of surface) will be $q=\rho \lambda \frac{d\delta}{dt}$, where $\rho$ is the liquid water density, and $\lambda$ is the heat of vaporization.  All this heat will be conducted across the condensed layer to the surface according to the equation:  $$q=\rho \lambda \frac{d\delta}{dt}=k\frac{(T_H-T_S)}{\delta}\tag{1}$$ where $T_H$ is the temperature of the steam (100 C), $T_S$ is the temperature of the surface of the flesh at time t (>> 37 C), and k is the thermal conductivity of water and flesh.  This heat will be conducted into the flesh, and, based on treating the flesh as a semi-infinite slab and assuming that the flesh surface temperature is constant during the heating, we would have $$q=k\frac{(T_S-T_C)}{\sqrt{\pi \alpha t}}\tag{2}$$where $T_C$ is the flesh temperature far from the surface (37 C) and $\alpha$ is the thermal diffusivity of the flesh and water $\alpha=k/(\rho c)$, with c representing the heat capacity.
Again assuming a constant flesh surface temperature, if we solve Eqn. 1 for the condensate layer thickness as a function of time, we obtain:  $$\delta=\sqrt{\frac{2k(T_h-T_S)}{\rho \lambda}}\tag{3}$$
Combining this with Eqns. 1 and 2 then yields:
$$(T_H-T_S)=(T_S-T_C)^2\frac{2c}{\pi \lambda}$$
Note that this equation no longer involves the time t, implying that the assumption of a constant flesh surface temperature was a correct one.  Dividing the equation by the overall temperature difference $(T_H-T_C)$ yields:  $$1-f=f^2\xi$$where f is the fractional approach $f=\frac{T_S-T_C}{T_H-T_C}$ and $\xi=\frac{2c(T_H-T_C)}{\pi \lambda}$ is the key dimensionless group for the heat transfer problem.
If we solve these equation for the fractional approach f and the flesh surface temperature, based on values of c = 4.184 kJ/kg-C and $\lambda$ = 2500 kJ/kg, we obtain a fractional approach of 0.68 and  a flesh surface temperature of 80 C.  This exceeds the value for contact with water at 100 C, 68.5 C, by more than 10 C.
A: TL;DR: You have probably not been exposed to 100°C water in either phase and even if you had, you could not have reasonably felt its temperature on account of receiving a third-degree burn. Hot water and steam are both dangerous but fundamentally different, so comparing them is like gorilla vs. shark.
I am not exactly sure what you are comparing here, but if you take a sufficiently large piece of your skin and expose it to 100 °C water (in either phase) for a sufficiently long time for your temperature sensors to actually give a reasonable result, you would suffer from a severe burn.
In this case, I have several reasons to distrust your reports about what temperature you feel.
(Note that by feel, I refer to your direct sense of temperature and not to the effects of the resulting injuries and similar.)
For example, this Healthline article reports 1 s of exposure to 69 °C water to be sufficient for a third-degree burn, which destroys your nerve endings and thus is mostly painless on the long run (and I doubt anybody can distinguish the nuances of extreme pain occurring before).
Now, what did you actually experience?

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*Sipping a cup of hot tea doesn’t give you 100 °C water.
Even if you brewed the tea with boiled water, the latter probably wasn’t homogeneously 100 °C to begin with.
It then cooled down during brewing the tea, pouring and through contact with the cup.
Sipping brings a very small amount of water in contact with your skin that gets cooled down through contact with skin and air rapidly (on account of being so small).
On top, you may have an additional protective layer of saliva or similar that needs to heat up before anything important does (pointed out by Shmuel Newmark).
What your temperature sensors perceive mostly depends of the amount of water.


*I am not sure what your steam experience is, but immersing any part of the body in pure 100 °C gaseous water is pretty difficult (and dangerous).
The steam that forms above pots or kettles with boiling water and anything else that is colloquially called steam is a mixture of gaseous water, air, and liquid water droplets.
The latter is what you can actually see; pure gaseous water is transparent.
Conversely, if you can see it, it’s not pure gaseous water, and I would be impressed if you actually managed to temperature-sense that with your skin.
Instead, if you boil a kettle of water, the steam that comes out has already considerably cooled down due to contact with the air and other factors.
It can still cause severe burns though.
If your exposure is sufficiently mild that it doesn’t, it depends on the details, i.e., how hot was the steam and how much was it, etc.
In general, your temperature perception depends on the amount of heat deposited on a timescale relevant to your heat sensors.
This in turn depends on:

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*The temperature of whatever you come in contact with.
Note that temperature is not simply “average kinetic energy” (see this question).

*The heat capacity, i.e., the amount of energy stored per temperature.
Liquid water has about twice the heat capacity per mass as gaseous water.
The differences of the heat capacity per volume are much bigger as the gas is much less dense.
For gaseous water, there also is the latent evaporation heat it can transfer to your body by condensing.

*The heat conductivity, i.e., how fast heat gets transferred between different layers of the substance and from the substance to your skin.
The heat conductivity of liquid water is about thirty times that of gaseous water.
However, gaseous water is much less viscous and thus can easily enter your pores to transfer heat to your skin, which is considered to be a major factor affecting the severity of steam burns (Science News: Understanding steam burns).


These vaporised molecules, possessing same energy of water (is at same temperature as it) plus latent heat of vaporisation, is what I am referring to as steam. So, it has more energy but same temperature.

Water vapour in air does not have to be at 100 °C or hotter.
Rather it has the temperature of the surrounding air.
You can think of it as water dissolved in air.
It exists at all temperatures and causes (or rather is) humidity.
The amount of water you can dissolve in air depends on the temperature.
Now due to changes in temperature, it can happen that a portion of air has more water dissolved in it than it can hold.
In that case, the water condenses to droplets you see as steam, clouds, or fog – not there is a fundamental difference between those.
If you boil water, you do indeed release packets of 100°C water vapour into the air, but these immediately cool down when mixing with the air, which causes condensation leading to the visible clouds we usually associate with steam.
Those are not 100°C hot (and nothing inside them is); if they were, your air would also have that temperature and you would not see much.
(The heating also causes an upward flux of air, which carries those droplets with it and avoids them returning to the water immediately.)

But now that it has, let me mention that this is a common secondary textbook fact, that is taught and studied in India. Here is a link to a related school material: https://byjus.com/questions/what-produces-more-severe-burns-boiling-water-or-steam/.

Both, boiling water and hot steam are pretty dangerous and how dangerous exactly depends on how long you are exposed to how much of it at what temperature and more.
As one is a liquid and one is (mostly) a gas, encounters with them are not directly comparable (as opposed for example to putting your arm in two different liquids).
You might as well ponder whether a gorilla would win a fight against a shark.
We might look at how much reported injuries we get for either, but that says more about how careless people are around the respective substances.
A: What we define as "hot" or "cold" is the transfer of energy -- how much (quantity) and how fast (rate of transfer) -- and how it raises our temperature. The more energy that is transferred from the object quickly, the hotter the object feels.
First, steam is in a vaporized phase -- which is why it has more energy. At 100 Celsius, water can exist both in gaseous and liquid phases. However, to vaporize liquid water, an energy input is required. This energy (called vaporization energy) is specific to each material, but if added, won't raise the temperature, but will simply vaporize the liquid into a gas. So, by vaporizing 100C water, you have water vapor at 100 degrees. Similarly, you can condense this vapor, by removing that same amount of energy required to vaporize it. In that case, you'd recover water at 100 degrees.
When you touch something hot, it will transfer heat to you until the temperatures have equalized. So when you touch hot water, the water will simply transfer whatever energy it needs to reach your hand's surface temperature (which won't happen, you'll take your hand out much sooner). However, when you touch steam, it will also transfer the condensation energy to you -- which is actually a lot of energy. This energy drastically raises your hand's the temperature, and you feel it as "hot."
Consider the simple heat transfer equation: the heat transfer rate $H$ is $$H=kA \dfrac{T_\text{hot}-T_\text{cold}}L$$
$L$ is unimportant for our case. What is important is $k$, the thermal conductivity constant -- this constant depends on the material. The higher this constant, the faster heat gets transferred, so more heat gets transferred, and your hand's temperature increases.
Next, $A$ represents the contact area between the surfaces. As @Wrzlprmft points out, steam can more easily enter skin pores. This will ensure more heat is transferred, since the total contact area is greater.
We can also maximize heat transfer by increasing the temperature difference, $T_\text{hot}-T_\text{cold}$. The greater this difference, the greater the heat flow. Note that as heat flows, this difference will shrink. In the case of water, $T_\text{hot}$ gets lowered and $T_\text{cold}$ gets higher. However, with vapor at 100C, the condensation energy leaves the vapor first, without changing the gas's temperature, so $T_\text{hot}-T_\text{cold}$ shrinks more slowly; $T_\text{hot}$ does not change, and thus, heat transfer is faster. Furthermore, the condensation energy is, for lack of a better word, quite large, which means that a lot will be transferred at that high rate.
TLDR: The reason steam feels hotter, is that it can transfer more energy to us faster (that is, without decreasing its temperature by transferring condensation energy), whereas water cannot. Our feeling of what's hot is determined by how much energy and how quickly an object transfers that energy to raise our temperature.

Edit: I forgot to mention that unlike water, steam can be packed tightly because it is a gas. Depending on how compressed the steam is in a given volume, you may experience 100C steam to feel warmer or colder than 100C water. For the purpose of my answer, I assumed the steam to be dense and tightly packed -- which can eventually make up for steam's lower thermal conductivity constant.
A: First point:
How hot or cold something feels doesn't purely depend on temperature. Temperature is just an (extensive) measure of the contained thermal energy amount. Rather, the important property is thermal conductivity for solids during conduction and the similar heat transfer coefficients for liquids and gases during convection. That is, the ability of the material to deliver the energy to your hand when you touch it. Look up aerogel as an example: while glowing hot thousand of decrees Celsius hot, straight out of the furnace, it can be held in your hand due to its very low thermal conductivity.
Second point:
Steam does contain more energy than water when both are at the same temperature. Because the steam apart from its thermal energy content also has absorbed latent heat energy for the phase change from liquid to gas. When you touch it, then for both the water and the steam you must absorb enough energy to reduce the temperature to that of your hand. But for the steam you first have to absorb energy to transform it from gas to liquid again. So you are in total absorbing more energy when touching the steam. If that happens fast - faster than how quick your hand can transfer the energy away from the surface skin - then the temperature of your skin will increase and you might burn.
A: If you were to actually feel both liquid water at 100C, and true steam(not some Water vapor in air) at 100C, then the water will feel hotter.
Note that the stuff that comes out of a kettle is not steam.
Note that a sauna is not filled with steam.
Because the water will inflict a first-degree burn in 0.25 seconds, causing pain.
But the burn will take almost 30 seconds to progress to third degree, where the pain will stop due to complete destruction of the nerves.
Steam, while at the same temperature, will not cool off in contact with your skin. It will remain at 100C as it converts to liquid, releasing the same energy as cooling the mere water from 100C to 0C, 4 times over.
A direct steam burn will cause third degree burns within 5 seconds, stopping the pain.
Thus, steam "feels" less hot than water, at 100C
I strongly suspect the OP is asking the difference is sensation between moderately hot hater (70C tea water), and the wafts of water vapor over a boiling pot (~ 20C above room temperature)
A: If feels hotter because though the temperature is the same, it really is "hotter" in the sense of having more heat in it to pour into your skin.
Steam burns you thrice over because the process of turning from steam back to water puts out a certain anount of heat into your flesh all by itself without changing temprature.
In 100° water, you're cooling the water with your flesh, and conversely the water is burning your flesh.
In 104° steam, you're cooling the steam with your flesh to 100°, THEN condensing it with your flesh, from 100° steam to 100° water,and THEN cooling the 100° water with your flesh.
It's the reverse of boiling, and you notice, when you are boiling water, you keep adding heat but the water doesn't go past 100°C. The heat you're adding isn't going into the temprature rising, but the boiling itself.
A: I think you've probably confused the question a little. Steam at 100 °C wont feel hotter than water at 100 °C, because it has a much lower thermal conductivity. However, steam in general can feel much hotter than water at 100 °C, because steam can be much hotter than 100 °C. In fact steam can even be hot enough to ignite paper.
A: It takes 500% as much energy to convert 100'C liquid water to 100'C steam, as it takes to bring freezing 0'C water to 100'C.

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*To raise 1g from 0'C to 100'C takes 418 Joules.

*To vaporise 1g of water from 100'C takes 2260 Joules.

Check that by timing a pan of water. It will take 5 times as long to steam off a liter of water as it takes to boil it!
So when you condense steam onto your hand, every drop releases more than 5 times the energy compared to spilling a drop of water on your hand.
We can nearly say that condensing 1g steam on your hand is like spilling theoretical 500'C water on it, because nearly all the dissociation energy of the steam molecules is released as heat when the water atoms coalesce again.
A: Note that steam doesn't feel hotter than water (as long as you consider steam at 100 degrees which is the case for steam under air pressure, contrary to steam in pressure cooking pans). The steamy droplets of steam have the same temperature as the boiling water they come from. Maybe a very small amount of latent heat is released. But not enough to make its temperature rise significantly. But even when it did have a higher temperature than water, the steam droplets are too much diluted in the air to do any harm.
If you put your hand in a boiling cup of water you'll probably give a scream. If you enter a (s)team-filled sauna (with an air temperature of 100 degrees Celsius) though you will probably not scream (if you don't look at the other people). That means that steam (when not in motion) is a worse conductor of heat than water. It consists of small water droplets but because there are not as much in a unit volume it will not pull much heat out of you. Only if you blow the steam towards your skin will you give a scream. In that case, all the droplets will meat your skin as one layer of water, causing it to pull the heat out of you.
To put it in a nutshell, steam has a much lower heat conductivity than water, which is why steam sucks less heat out of you than water. Why is steam a worse conductor of heat than water? because of the air surrounding the steam. Air conducts heat very badly, so the net result of both the drops and air (steam) will be that it's a worse conductor than water. If you would look at the drops only, then obviously it could pull heat out of you. Luckily, the drops are not 1(cm) big. This would be hot rain and would surely harm you.
