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a. Calorific value of coal in a bomb (Qb) The calorific value of coal in a bomb refers to the heat generated per unit mass of coal sample when it burns inside a bomb-type calorimeter under excessive high-pressure oxygen (around 25–35 atmospheres), with the final temperature of the combustion products set at 25°C. Since the coal sample was burned in a cylinder filled with high-pressure oxygen, thermochemical reactions that do not occur when coal burns in air took place. For example, nitrogen in coal and nitrogen in the air inside the cartridge before oxygen is introduced generally escapes as gaseous nitrogen when burning in air, whereas when burning in the cartridge, nitrogen oxides such as N2O5 or NO2 are formed. These nitrogen oxides dissolve in the cartridge tax to form nitric acid; this chemical reaction is exothermic. Furthermore, when the combustible sulfur in coal burns in air, it produces SO2 gas that escapes, whereas when it burns in the cartridge, it is oxidized to SO3; SO3 then dissolves in the water in the cartridge to form sulfuric acid. The dissolution of SO2, SO3, and H2SO4 in water to form sulfate hydrates are all exothermic reactions. Therefore, the calorific value of coal in a bomb is higher than the actual heat generated when the coal burns in air or in industrial boilers. To this end, in practice, the heat release of the cartridge must be converted into a value corresponding to that of coal burning in air. b. High calorific value of coal (Qgr) The high calorific value of coal refers to the heat generated when coal burns under atmospheric pressure in air. In fact, it is the heat obtained by subtracting the heat of formation of sulfuric acid and nitric acid from the bomb calorific value of coal measured in the laboratory. It should be noted that the calorific value of coal in a bomb is measured under constant volume conditions (i.e., with the volume of the combustion chamber inside the bomb remaining unchanged), which is why it is also known as the constant-volume bomb calorific value. The higher heating value calculated from the heat released in a constant-volume bomb is also known as the constant-volume higher heating value. Coal burns under atmospheric pressure in air under conditions of constant humidity and pressure (with the atmospheric pressure remaining unchanged); its high calorific value is the high calorific value at constant humidity and pressure. There is a difference between the constant-volume higher heating value and the constant-pressure higher heating value. Generally, the high-heating value at constant volume is 8.4–20.9 J/g lower than that at constant pressure; in practice, when high precision is not required, no correction is usually made.
These two concepts are often easily confused; the original poster has provided a fairly detailed explanation in this post