The new experiment calculates the combustion rate of carbon element by using the content of CO and CO_{2} in the gas, that is, to calculate the proportion of CO and CO_{2}. The formula is deduced as follows:

Assuming that the pulverized coal sample contains *N* mol of carbon, which has *X* mol of carbon to produce *X* mol CO_{2}, *Y* mol of carbon to produce *Y* mol CO, obviously *N* ≥ *X*+*Y*. So the combustion rate is:
$\eta =\frac{X+Y}{N}$(1)

In the experiment, *M* mol gas (including the gas that did not contact with pulverized coal before entering into the gas cylinder and the gas contacted with pulverized coal) was introduced into the gas cylinder. *X* mol CO_{2} was generated by *X* mol carbon, and *X* mol O_{2} was consumed at the same time, so there is no effect on the number of moles of gas in the gas cylinder. Similarly, SO_{2} generated by combustion of sulfur element has no effect on the number of moles of gas in the gas cylinder. *Y* mol CO was generated by *Y* mol C, while *1/2Y* mol O_{2} was consumed at the same time. In addition, a part of hydrogen, oxygen and nitrogen of coal decomposed *q* mol gas, So the total production of gas was (Y–1/2Y+q) mol. That is (1/2Y+q) mol. Therefore, when *N* mol carbon was partially burned to produce *X* mol CO_{2} and *Y* mol CO, the moles of gas in the cylinder are *M+1/2Y+q* mol.

Supposing that ${\phi}_{C{O}_{2}}$ and ${\phi}_{CO}$ are the mole fractions of CO_{2} and CO of the combustion exhaust gas in the cylinder, so:
${\phi}_{C{O}_{2}}=\frac{X}{M+1/2Y+q}$(2)

${\phi}_{CO}=\frac{Y}{M+1/2Y+q}$(3)${\phi}_{CO}+{{\phi}_{CO}}_{{2}_{}}=\frac{X+Y}{M+1/2Y+q}$(4)When the *N* mol carbon is completely combusted to produce *N* mol CO_{2}, the molar fraction of CO_{2} in the gas cylinder is:
${\phi}_{C{O}_{2}theory}=\frac{N}{M+Q}$(5)

*Q* is the total number of moles of gas dissolved in oxygen, oxygen and nitrogen of the coal, and can be calculated from the ultimate analysis data of coal.
$\begin{array}{c}\frac{{{\phi}_{CO}}_{{2}_{}}+{\phi}_{CO}}{{\phi}_{{CO}_{2}theory}}=\frac{(X+Y)(M+Q)}{N(M+1/2Y+q)}=\frac{X+Y}{N}\cdot \frac{M+Q}{M+1/2Y+q}\\ =\frac{X+Y}{N}(1-\frac{1/2Y}{M+1/2Y+q}+\frac{Q-q}{M+1/2Y+q})\end{array}$(6)

where the value of $\frac{Q-q}{M+1/2Y+q}$ is small, can be ignored, then:
$\frac{{{\phi}_{CO}}_{{2}_{}}+{\phi}_{CO}}{{\phi}_{{CO}_{2}theory}}=\frac{X+Y}{N}\left(1-\frac{1/2Y}{M+1/2Y+q}\right)=\frac{X+Y}{N}\left(1-\frac{1}{2}{\phi}_{CO}\right)$

So the combustion rate is:
$\eta =\frac{X+Y}{N}=\frac{{{\phi}_{CO}}_{{2}_{}}+{\phi}_{CO}}{(1-\frac{1}{2}{\phi}_{CO})\cdot {\phi}_{{CO}_{2}theory}}$(7)

The formula (7) is the formula for the calculation of the combustion rate of carbon in the New Experimental Equipment for Combustion of Pulverized Coal in Blast Furnace.

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