A $50\backslash$mu m diameter bituminous $($A$)$ char particle burns in product gas at

$1$ atm and $1600$ K$.$ As the particle burns to form carbon monoxide, the heat

release is $9200$ kJ$/$gchar$.$ The burning rate constant is $0\mathrm{.}05$ gO$2$

$/($cm$2$ s $$ atmO$2).$ Calculate the steady state surface temperature of the particle for oxygen particle pressures of $0\mathrm{.}06$ atm, $0\mathrm{.}13$ atm, and $0\mathrm{.}21$ atm. Account for convection and radiation heat loss from the particle. Assume that the particle emissivity is $0\mathrm{.}8,$ and use a Nusselt number of $2.$