For a $100\backslash$mu m bituminous $($C$)$ coal char particle with an oxygen partial pressure far from the particle of $0\mathrm{.}1$ atm, find the oxygen partial pressure at the

char surface when the gas temperature is $2000$ K$.$ Assume that the particle

temperature is $100$ K greater than the gas temperature and that there is no

relative velocity between the particle and the gas. Repeat for a gas temperature of $1500$ K