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GATE 2025 Chemical Engineering, Q39 · Process Control

The correct answer is C, 0.6.

Question

The first-order irreversible liquid phase reaction A → B occurs inside a constant volume (V) isothermal CSTR with the initial steady state conditions shown in the figure: CA0=2.5kmol/m3,C_{A0} = 2.5 kmol/m³, F =1m3/h,= 1 m³/h, V =10m3,CA=1.0kmol/m3.= 10 m³, C_{A} = 1.0 kmol/m³. The gain, in (kmol/m3)/(m3/h),(kmol/m³)/(m³/h), of the transfer function relating the reactor effluent A concentration, CA,C_{A}, to the inlet flow rate, F, is

Figure for Q39 (Process Control, Transfer Functions): The first-order irreversible liquid phase reaction A → B occurs inside a constant volume (V) isother…
  • A. 1.2
  • B. 0.4
  • C. 0.6
  • D. 0.8

Official answer: 0.6

Why

GATE 2025 official key: (C). Steady state: F⋅CA0=F⋅CA+kVCA⇒F\cdot C_{A0} = F\cdot C_{A} + kVC_{A} \Rightarrow k =F(CA0−CA)/(VCA)=1×1.5/10== F(C_{A0}−C_{A})/(VC_{A}) = 1 \times 1.5/10 = 0.15/h. CA(F)=FCA0/(F+kV);C_{A}(F) = FC_{A0}/(F+kV); gain =dCA/dF=CA0⋅kV/(F+kV)2=2.5×1.5/2.52=3.75/6.25=0.6.= dC_{A}/dF = C_{A0}\cdot kV/(F+kV)² = 2.5 \times 1.5/2.5² = 3.75/6.25 = 0.6.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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