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GATE 2024 Chemical Engineering, Q43 · Mechanical Operations

The correct answer is B, 2.55.

Question

Alumina particles with an initial moisture content of 5 kg per kg dry solid are dried in a batch dryer. For the first two hours, the measured drying rate is constant at 2kg/(m2⋅h).2 kg/(m²\cdot h). Thereafter, in the falling-rate period, the rate decreases linearly with the moisture content. The equilibrium moisture content is 0.05 kg per kg dry solid and the drying area of the particles is 0.5m20.5 m² per kg dry solid. The total drying time, in h, to reduce the moisture content to half its initial value is

  • A. 4.13
  • B. 2.55
  • C. 3.22
  • D. 5.13

Official answer: 2.55

Why

GATE 2024 official key: (B). Critical moisture: Xc=X0−a⋅Rc⋅tc=5−(0.5×2)(2)=3.X_{c} = X₀ − a\cdot R_{c}\cdot t_{c} = 5 − (0.5 \times 2)(2) = 3. Target Xfinal=2.5X_{final}=2.5 is below Xc,X_{c}, so it lies in the falling-rate period. tf=[(Xc−X∗)/(aRc)]⋅ln[(Xc−X∗)/(Xfinal−X∗)]=2.95×ln(2.95/2.45)≈0.548t_{f} = [(X_{c}−X*)/(aR_{c})]\cdot ln[(X_{c}−X*)/(X_{final}−X*)] = 2.95 \times ln(2.95/2.45) \approx 0.548 h. Total t =2+0.548≈2.55= 2 + 0.548 \approx 2.55 h.

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

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