The elementary reversible exothermic gas-phase reaction
A + 3B $\rightleftharpoons$ 2C
is to be conducted in a non-isothermal, non-adiabatic plug flow reactor. The maximum allowable reactor temperature is T${_m}{_a}{_x}$. To minimize the total reactor volume, the variation of reactor temperature(T) with axial distance from the inlet(z) should be
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