A first-order homogeneous liquid-phase reaction (A→B) occurs in an adiabatic, ideal mixed flow reactor at steady state. Feed flow rate is 4 L min⁻¹, reactor volume 20 L. At the reactor temperature of 500 K, k = 1 min⁻¹, and heat of reaction is −20 kcal mol⁻¹. The feed and reaction-mixture heat capacity is 0.3 kcal mol⁻¹ K⁻¹. The inlet feed temperature (in K) is _________ (rounded off to one decimal place).

Question

Accepted Answer

The correct answer is 443 to 446. GATE 2026 official key: 443.0 to 446.0. τ = 20/4 = 5 min; X = kτ/(1+kτ) = 5/6 = 0.833. Adiabatic balance: T − T0 = X(−ΔHrxn)/Cp = 0.833×20/0.3 ≈ 55.6 K, so T0 = 500 − 55.6 ≈ 444.4 K.