Bacillus subtilis growing on methanol has a maximum growth yield coefficient of $Y^M\frac{x}{s}=0\mathrm{.}45g\frac{x}{g}S.$ The heat of

combustion of cells is $5\mathrm{.}64$kca$\frac{l}{g}$ cells and for combusting the substrate $(H_c)$ is $7\mathrm{.}2$kca$\frac{l}{g}-$methanol.

A$.$ Determine the metabolic heat generated by the cells per unit mass of methanol consumption, $Y_{\frac{}{s}}($in kca$\frac{l}{g}$

S$).\{$Hint: see class notes $\}$

The cells are growing in the exponential growth phase in a $4\mathrm{.}5L$ chemostat reactor with a steady state cell

concentration of $[x]=10\mathrm{.}8\frac{g}{L}$ and a feed concentration of $28\mathrm{.}3\frac{g}{L}$ methanol, at the maximum specific growth

rate, ${}_{\text{m}\text{a}\text{x}},$ of $0\mathrm{.}87h^{-1}.$

B$.$ At what rate must heat be removed from the reactor to maintain an isothermal reactor $($in kca$\frac{l}{h}?$