GATE 2026 CH – Question 55
A first-order homogeneous liquid-phase reaction (A→B) occurs in an adiabatic, ideal mixed flow reactor operating at steady state. The volumetric flow rate of the feed is 4 L min$^{-1}$ and volume of the reactor is 20 L. At the reactor temperature of 500 K, the reaction rate constant is 1 min$^{-1}$, and heat of reaction is −20 kcal mol$^{-1}$. The average heat capacity of the feed as well as the reaction mixture in the temperature range of interest is 0.3 kcal mol$^{-1}$ K$^{-1}$.
At the inlet, the feed temperature (in K) is _________ (rounded off to one decimal place).
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Correct answer: 442.18 to 446.62
Explanation
The space time is $\tau = \frac{20}{4} = 5$ min. For a first order reaction in a mixed flow reactor, $X = \frac{k\tau}{1 + k\tau} = \frac{5}{6}$. The adiabatic energy balance per mole of feed is $C_p(T - T_0) = (-\Delta H_r)X$, so $T_0 = 500 - \frac{20 \times 5/6}{0.3} = 500 - 55.6 = 444.4$ K.