In a normal operation of the coal fired power plant, critical regimes exist where the particles cannot be ignited either in the gas mode or in the heterogeneous mode due to excessive heat loss. Following thermal theories of ignition, sufficient conditions for the extinction sizes for quenching gas phase combustion are presented along with critical limits for the gas phase and heterogeneous ignition of coal particles. Universal plots are given to present the critical parameters of both modes of ignition in terms of known physico-chemical data of any coal/char particle. Quantitative results for the critical size and oxygen concentration of brown coal particles estimated from the plots are found to check with the iterative numerical results carried out elsewhere. Such sizes and oxygen concentrations may serve as ignitability indices of different coal particles.