How is it possible that combustion of coal releases similar energy as TNT explosion while intuitively we would not expect that? According to Wikipedia, the energy released in a TNT explosion is 4 × 106 J/kg.
https://en.wikipedia.org/wiki/TNT
According to web, combusion of coal is around 24 × 106 J/kg.
https://www.world-nuclear.org/information-library/facts-and-figures/heat-values-of-various-fuels.aspx
This looks rather counter-intuitive: TNT is famous for the explosion, thus I would expect that it releases a lot of energy, but actually, it seems much smaller than coal combustion...
How is that possible that combustion of coal releases similar energy as a TNT explosion while intuitively we would not expect that?
 A: There are some marked differences that make $\text{TNT}$ far more suitable than the combustion of coal for explosives purposes.
Firstly, the decomposition reaction of $\text{TNT}$:
$$2 \text{C}_7\text{H}_5\text{N}_3\text{O}_6 \to 3 \text{N}_2 + 5 \text{H}_2 + 12 \text{CO} + 2 \text{C}$$
proceeds far faster than the combustion reaction of coal:
$$\text{C}+\text{O}_2 \to \text{CO}_2$$
Secondly, the decomposition of $\text{TNT}$  produces far more gaseous reaction products than the combustion of coal: respectively $10\text{ mol}$ of gas per $\text{mol}$ of $\text{TNT}$ for $1\text{ mol}$ of gas per $\text{mol}$ of coal (and the latter requires $1\text{ mol}$ of $\text{O}_2$ for the combustion to take place).
It's the production of gaseous reaction/decomposition products that make a good explosive: the super-fast build-up of gas inside the shell makes the pressure increase until the shell bursts, releasing all its energy at once.
A: An explosion is, abstractly, the occurrence of a high rate of energy transformation in time: A lot of energy is "released" (that is, transformed from chemical or nuclear energy to radiation and heat) within a short interval. It is important enough that physics has a name for such a "energy density in time": Power.
Energy is more interesting when it is concentrated, also in space: A laser is more interesting than a diffuse light source, even though both may release the same amount of radiation over time. Here entropy comes into play: Concentrated energy is "usable" (the energy flow occurring when the entropy grows — i.e., when the concentrated energy disperses — can be put to use).
Because of limitations like the speed of the proliferation of nuclear and chemical reactions, and ultimately the speed of light, one requirement for a high-power explosion — a high concentration of energy in time — is a high concentration of energy in space beforehand.
A: Probably because the energy released by the TNT explosion is for a very short time whilst the energy released from combustion of coal is over a much longer time. It’s the energy release rate of the TNT that’s greater

Thank you. But do i understand that the increase of temperature is
bigger with coal than with TNT ?

That's hard to say since it would be difficult to specify a single temperature of the rapidly expanding gases and particles of the explosion. There would be significant temperature (and pressure) gradients in an explosion compared to the burning of coal. The temperature of the burning coal would be more uniform.
Hope this helps
A: First, there is a key difference between the energy values of TNT and coal: you miss the oxygen needed to burn the coal.
Burning 3kg of coal needs some 8kg of oxygen and the oxygen is not included in the calorific value above. The oxygen is also the factor limiting how fast the coal releases its energy. It is limited by the supply of oxygen.
That's why coal by itself cannot do much of destruction.
In contrast, when detonated, TNT decomposes by itself. It can also burn pretty well, but that's another story completely.
OTOH, there are a class of explosives made of some fuel (like coal) and a liquid oxygen. They are not routinely used anymore because of safety and logistics concerns, but they are more or less comparable to TNT in regard to their explosive action.
When you have everything for the chemical reaction to proceed in close proximity, an explosion is possible.

Edit:
Another, much more known and widely used explosive that uses coal as a main ingredient and a main source of combustion energy powering the explosion is the black powder.
A: The key difference between an explosion and a combustion is speed not energy produced
The key thing that matters for explosives is how fast the reaction proceeds. TNT detonates, which means that, in solid TNT, the reaction propagates through the solid faster than the speed of sound. Some slightly gentler explosives (like the propellants used for bullets and shells) also have fast propagation but slower than the speed of sound: they are said to deflagrate. In both cases the distinguishing feature is how fast they release their energy.
Explosives can do this because they involve reactions that don't need external substances to complete the chemical reaction involved in the process. They usually contain large amounts of oxygen and nitrogen in their molecular structure (which tend to lead to products containing nitrogen gas, nitrogen oxides, carbon dioxide and so on).
Coal burns slowly. It only burns when oxygen can get at the coal's surface. And coal, being a not very porous solid, doesn't make this easy for the oxygen. So the reaction might release more energy but the speed is limited to perhaps mm/min by the physical structure.
But not always. if coal dust (or indeed any other dust of a flammable material) is dispersed in air, the speed of oxygen diffusion is no longer a limiting factor. This is why dust explosions are very dangerous (and not just for coal: the commonest are in flour mills and grain silos). Coal dust in those conditions can detonate and release catastrophic amounts of energy very quickly.
It is also worth noting that the largest known non-nuclear bombs used by the military are based on a similar principle. Thermobaric bombs involve dispersion of some fuel (like a liquid hydrocarbon with even more combustion energy than coal) to a fairly precise level in air where the resulting mixture will explode rather than combust. This is not the usual behaviour for combustible fuels like gasoline as getting an explosive mixture in air rather than one that will just burn is not easy (which is why the every-car-crash-explodes movie trope is nonsense). So getting the right mix of fuel and air can yield a very big explosion even more effective than TNT.
in short, to understand explosions you need to think kinetics not just thermodynamics of the underlying reactions.
A: You’re basically talking about the difference between power and energy. A TNT explosion has vastly more power than the combustion of an equivalent amount of coal (in normal circumstances), because it happens over a vastly shorter timescale. And it’s the power that you notice, not the energy.
