The thermal structure of a particle burning in the diffusion limit is shown in Fig. 2, where the temperature at the particle surface approaches the stoichiometric adiabatic flame temperature of the particle-gas reaction while the bulk gas remains relatively cool. And the adiabatic equation p/r γ = const, where p, ρ, and T are the gas pressure, density, and temperature, R the universal gas constant, the gas molecular mass, and γ the adiabatic exponent which, for an ideal gas, is determined as the ratio of heat capacities at a constant pressure and volume γ = c p /c v with c p – c v =. The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate, the average translational kinetic energy of a freely moving particle in a system with temperature T will be 3k B T/2.

1. Temperature Adiabatic Size Particle Dimensions
2. Temperature Adiabatic Size Particle Model

Temperature Adiabatic Size Particle Dimensions

Temperature Adiabatic Size Particle Model

Reaction rate depends upon three things: temperature (higher temperature means faster reactions), particle size (smaller particles leading to an increase in surface area means faster reactions) and concentration of reactants (the higher the concentration, the higher the chance for particle collisions). Rate of reaction is based upon particle collisions. Higher temperatures yield more and stronger collisions, hence there is higher rate of reaction. Smaller particles (giving more surface area) means more collisions (reactants are not.