In a continuous contacting device, the operating line is obtained from which fundamental principle?
Answer: A
Operating line represents all possible compositions entering and leaving the device based on material balance: Y₁ - Y₂ = (L/V)(X₁ - X₂)
Q.22Medium
The penetration theory for mass transfer assumes that:
Answer: A
Penetration theory (Higbie) assumes eddies contact interface, remain for time θ, then submerge. More realistic than film theory for turbulent systems.
Q.23Medium
For simultaneous heat and mass transfer in a cooling tower, the Lewis number (Le = α/D) typically has a value of:
Answer: A
For air-water system: Le = α/D ≈ 0.8-1.0. This means heat and mass transfer coefficients are comparable, important for cooling tower design.
Q.24Medium
In distillation, the Murphree plate efficiency is defined as the ratio of:
Answer: A
E_mv = (y_n - y_(n-1))/(y*_n - y_(n-1)), where y* is equilibrium vapor composition. Accounts for non-equilibrium stage behavior.
Q.25Medium
For gas absorption in a plate column, the gas-phase mass transfer coefficient increases with:
Answer: A
Higher velocity increases turbulence (higher k); lower pressure increases diffusivity D. Both increase Sh = kL/D.
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Q.26Medium
The concept of 'equivalent theoretical stages' in absorption is based on:
Answer: A
Used to compare different types of contactors. Actual stages divided by Murphree efficiency gives equivalent theoretical stages needed.
Q.27Medium
In evaporative cooling, the effectiveness (ε) is defined as:
Answer: A
ε = (t_in - t_out)/(t_in - t_wb). Higher effectiveness indicates better utilization of air capacity, crucial for cooling tower design.
Q.28Medium
In membrane separation processes, the selectivity is expressed as:
Answer: A
Selectivity α = (J_A/ΔP_A)/(J_B/ΔP_B). Higher selectivity indicates better separation capability of the membrane.
Q.29Medium
The Fick's first law of diffusion in binary mixtures states that the molar flux J_A is proportional to:
Answer: B
Fick's law: J_A = -D_AB(dC_A/dz) + C_A(J_A + J_B). The total flux includes both diffusive and convective contributions due to bulk flow.
Q.30Medium
For equimolar counter-diffusion in a binary system, the molar fluxes satisfy:
Answer: D
In equimolar counter-diffusion, moles of A diffusing in one direction equal moles of B diffusing in the opposite direction, making J_A = -J_B and their sum zero.
Q.31Medium
The Stefan problem in mass transfer involves:
Answer: A
The Stefan problem deals with unsteady diffusion with a moving interface, commonly encountered in evaporation from droplets and sublimation processes where the interface position changes with time.
Q.32Medium
In a countercurrent absorption column, if the gas-phase mass transfer coefficient is k_G = 0.05 kmol/(m²·s·atm), the interfacial area 'a' = 200 m²/m³, and column cross-section = 5 m², the volumetric overall mass transfer coefficient is:
Answer: B
Overall volumetric mass transfer = k_G × a × Volume = 0.05 × 200 × (5 × height). For unit height, K_G·a·V = 0.05 × 200 × 5 = 50 kmol/(s·atm).
Q.33Medium
The penetration theory for mass transfer assumes that the contact time between fluid elements is:
Answer: B
Penetration theory assumes fluid elements contact the interface for a short time, then move away. Mass transfer is modeled using unsteady diffusion into a semi-infinite medium.
Q.34Medium
For absorption of a sparingly soluble gas in a liquid with fast reaction kinetics, the enhancement factor 'E' is determined by:
Answer: B
The enhancement factor E = k_L,with reaction/k_L,without reaction depends on the Hatta number (Ha = √(k·C_A0·D_A/k_L²)), which incorporates reaction kinetics and mass transfer parameters.
Q.35Medium
In membrane separation, the permeate flux in reverse osmosis is given by:
Answer: B
The reverse osmosis permeate flux follows: J = A(ΔP - Δπ), where A is membrane permeability, ΔP is applied pressure, and Δπ is osmotic pressure difference.
Q.36Medium
A gas A diffuses through a stagnant film of gas B. If the diffusivity D_AB = 0.1 cm²/s, film thickness δ = 0.01 cm, and concentration difference = 0.05 mol/cm³, the diffusive flux is:
Answer: B
Using Fick's law for stagnant diffusion: J = D_AB·ΔC/δ = 0.1 × 0.005.01 = 0.5 × 10⁻² = 5 × 10⁻³ mol/(cm²·s).
Q.37Medium
The height of a transfer unit (HTU) in a packed absorption column represents:
Answer: B
HTU = V·G/(k_G·a·A), where a smaller HTU indicates more efficient mass transfer. It represents the column height needed to achieve one logarithmic unit of concentration driving force reduction.
Q.38Medium
In a binary gas mixture, if component A is highly soluble in the liquid phase compared to component B, which statement is true regarding absorption?
Answer: C
High solubility of A means low liquid-phase resistance for A, making the gas-phase resistance dominant. Thus, gas-phase mass transfer resistance controls the overall rate for A.
Q.39Medium
For absorption of sparingly soluble gas in a liquid film, the operating line and equilibrium curve relationship determines:
Answer: B
The vertical distance between operating and equilibrium lines represents the concentration driving force, determining whether absorption occurs and in which direction.
Q.40Medium
In distillation, the Murphree plate efficiency is always:
Answer: B
Murphree plate efficiency accounts for non-ideal mixing on a plate, therefore it is always less than or equal to the overall efficiency which includes effects of all plates.
