Burning of coal is represented as  ${\mathrm{C}}_{\left(\mathrm{s}\right)}+{\mathrm{O}}_{2_{\left(\mathrm{g}\right)}}\to {\mathrm{CO}}_{2_{\left(\mathrm{g}\right)}}$. The rate of this reaction is increased by

FACTORS AFFECTING THE RATE OF REACTION: 
(i) Concentration : Law of mass action enunciates that greater is the conc. of the reactants, the more rapidly the reaction proceeds.

(ii) Pressure (Gaseous reaction) : On increasing the pressure, volume decreases and conc. increases and hence the rate increases.

(iii) Temperature : It is generally observed that rise in temperature increases the reaction rate.

(iv) Nature of the reactants : The rate depends upon specific bonds involved and hence on the nature of reactants.

(v) Surface area of the reactants : In heterogeneous reactions, more powdered is the form of reactants, more is the velocity. [as more active centres are provided]

So, the rate of reaction will increase by powdering the lumps of coal as surface area increases in that case.