In a parallel plate channel with constant heat flux q'' on both walls, what is the thermal entrance length relationship with hydrodynamic entrance length?

The correct answer is A: L_th = L_h/Pr. Thermal entrance length L_th ≈ L_h/Pr for laminar flow, where Pr < 1 for metals means thermal entrance is shorter than hydrodynamic entrance.

The mutual diffusivity D_AB of a binary system is NOT a function of which of the following?

The correct answer is C: Composition (mole fractions x_A, x_B). According to kinetic theory, D_AB depends on T, P, and molecular properties (mass, size, collision diameter) but NOT directly on composition in ideal systems (though real systems may show weak composition dependence).

A surface at 300 K with emissivity 0.8 radiates heat to surroundings at 250 K. Calculate the net radiative heat transfer per m² (σ = 5.67 × 10⁻⁸ W/m²·K⁴).

The correct answer is B: 247.3 W/m². Net radiation Q = ε·σ·(T₁⁴ - T₂⁴) = 0.8 × 5.67 × 10⁻⁸ × (300⁴ - 250⁴) = 0.8 × 5.67 × 10⁻⁸ × (8.1×10⁹ - 3.9×10⁹) = 247.3 W/m²

In evaporative cooling, the heat and mass transfer are coupled. The Lewis number (Le) relationship between them is:

The correct answer is B: Le = Sc/Pr, determines coupling extent. Lewis number Le = Sc/Pr = (ν/D_AB)/(α/ν) = ν/(D_AB·α). For air, Le ≈ 1, meaning heat and mass transfer are equally significant in coupled processes.

Which of the following materials would be most suitable for a heat sink application requiring high thermal conductivity and low cost?

The correct answer is B: Aluminum alloy (k = 160 W/m·K). Aluminum alloys offer an excellent balance of thermal conductivity (160 W/m·K, sufficient for most applications), cost-effectiveness, light weight, corrosion resistance, and ease of machining. While copper has higher conductivity, aluminum's cost-benefit ratio is superior for heat sink applications.

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Chemical Engineering

Process design, thermodynamics, reactions

117 Q 5 Topics Take Mock Test

Difficulty: All Easy Medium Hard 101–110 of 117

Topics in Chemical Engineering

All Mass Transfer 100 Heat Transfer 100 Fluid Mechanics 100 Chemical Reaction Engineering 100 Thermodynamics 97

Q.101 Hard Mass Transfer

In coal gasification combustion analysis (2024-25 focus), the mass transfer of oxygen to solid particles is characterized by:

A External film resistance and particle surface reaction kinetics

B Only diffusion through ash layer

C Pressure variations alone

D Temperature-independent process

Correct Answer: A. External film resistance and particle surface reaction kinetics

EXPLANATION

Shrinking core model applies: external diffusion, ash diffusion, and chemical reaction all contribute. Modern focus on clean energy requires optimized design.

Test

Q.102 Hard Mass Transfer

For a reverse osmosis process, the concentration polarization effect results in:

A Higher salt concentration at membrane surface than in bulk solution

B Lower salt concentration at membrane surface

C No change in concentration profile

D Uniform concentration throughout the module

Correct Answer: A. Higher salt concentration at membrane surface than in bulk solution

EXPLANATION

Due to higher solute rejection, solutes accumulate near membrane surface, increasing local osmotic pressure and reducing driving force.

Test

Q.103 Hard Mass Transfer

The Thiele modulus (Φ) for a catalyst pellet determines whether the reaction is:

A Diffusion-limited (high Φ) or kinetically-limited (low Φ)

B Always limited by surface area

C Independent of pellet size

D Dependent only on reaction rate constant

Correct Answer: A. Diffusion-limited (high Φ) or kinetically-limited (low Φ)

EXPLANATION

Φ = L√(k/D). When Φ >> 1, diffusion controls; when Φ << 1, kinetics controls. Critical for reactor design optimization.

Test

Q.104 Hard Mass Transfer

For a pseudosteady-state diffusion with heterogeneous reaction, the effectiveness factor η accounts for:

A The reduction in reaction rate due to limited diffusion to active sites

B The increase in reaction rate due to surface effects

C The ratio of actual conversion to theoretical conversion

D The pressure drop in the catalyst bed

Correct Answer: A. The reduction in reaction rate due to limited diffusion to active sites

EXPLANATION

η = (actual reaction rate)/(rate if all surface at bulk concentration). Important in catalytic reactors where diffusion and reaction compete.

Test

Q.105 Hard Mass Transfer

The Colburn analogy relates dimensionless groups for mass, heat, and momentum transfer as:

A j_D = j_H = f/2, where j represents the Colburn factor

B All three j factors are always equal

C j_D depends on Le while j_H depends on Pr

D They are unrelated for engineering purposes

Correct Answer: A. j_D = j_H = f/2, where j represents the Colburn factor

EXPLANATION

Colburn analogy: j_D = (Sh)/(Re·Sc^(1/3)) ≈ j_H ≈ f/2 for smooth surfaces. Useful for correlating data when only one phenomenon is studied.

Test

Q.106 Hard Mass Transfer

In ion exchange resins, the mass transfer resistance primarily occurs in:

A The particle pore structure (pore diffusion)

B The external liquid film

C The ion exchange reaction itself

D The resin backbone structure

Correct Answer: A. The particle pore structure (pore diffusion)

EXPLANATION

For ion exchange, intraparticle diffusion through pores is the rate-limiting step. External film resistance is negligible in comparison.

Test

Q.107 Hard Mass Transfer

For a binary gas mixture, the Stefan flow correction factor accounts for:

A Net molar flow due to unequal molar diffusion rates

B Pressure variations in the system

C Temperature gradients across the interface

D Viscosity changes with composition

Correct Answer: A. Net molar flow due to unequal molar diffusion rates

EXPLANATION

When one component condenses/reacts, equal molar counter-diffusion assumption breaks down. Stefan factor (B_m) corrects for net molar flow.

Test

Q.108 Hard Mass Transfer

For a hollow fiber membrane contactor used in gas-liquid mass transfer, the overall mass transfer coefficient K_OL is related to individual coefficients by:

A 1/K_OL = 1/k_G + m/k_L

B 1/K_OL = 1/k_L + 1/(m*k_G)

C K_OL = k_G + k_L

D K_OL = (k_G * k_L)/(k_G + k_L)

Correct Answer: B. 1/K_OL = 1/k_L + 1/(m*k_G)

EXPLANATION

For gas-liquid systems, 1/K_OL = 1/k_L + 1/(m*k_G), where m is the distribution coefficient. This accounts for both liquid and gas side resistances.

Test

Q.109 Hard Mass Transfer

For simultaneous momentum and mass transfer in a boundary layer, the Chilton-Colburn analogy relates j_D to friction factor f_D by:

A j_D = f_D / 2

B j_D = f_D

C j_D = 2 * f_D

D j_D = f_D * Sc^(1/3)

Correct Answer: A. j_D = f_D / 2

EXPLANATION

The Chilton-Colburn analogy states that j_D = j_H = f_D/2, assuming equivalent Pr and Sc values, relating mass transfer to friction factor.

Test

Q.110 Hard Mass Transfer

For a dilute binary gas mixture diffusing through a stagnant layer, the diffusion coefficient D_AB can be estimated using the Chapman-Enskog theory. Which statement is correct?

A D_AB is independent of pressure

B D_AB is inversely proportional to pressure

C D_AB is directly proportional to pressure

D D_AB is independent of temperature

Correct Answer: B. D_AB is inversely proportional to pressure

EXPLANATION

According to Chapman-Enskog theory, D_AB ∝ T^(3/2)/P for gases. Thus, D_AB is inversely proportional to pressure at constant temperature.

Test

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