The relationship between mass transfer coefficient and diffusivity is given by the Chilton-Colburn analogy. If diffusivity doubles while other conditions remain constant, how does the mass transfer coefficient change (assuming laminar flow)?

The correct answer is A: Increases by √2 times. In laminar flow, k ∝ D^(1/2). Therefore, if D doubles, k increases by √2 times (approximately 1.414 times).

The Sherwood number (Sh) in mass transfer correlations represents the dimensionless:

The correct answer is B: Ratio of convective to diffusive mass transfer. Sherwood number Sh = k_c·L/D_AB represents the ratio of convective mass transfer to diffusive mass transfer, analogous to Nusselt number in heat transfer.

For a horizontal pipe with diameter variation from D₁ to D₂, if pressure difference is ΔP and ignoring losses, the velocity ratio V₁/V₂ is:

The correct answer is B: (D₂/D₁)². By continuity: A₁V₁ = A₂V₂. Since A = πD²/4, we get V₁/V₂ = A₂/A₁ = (D₂/D₁)². Pressure difference from Bernoulli validates this for incompressible flow.

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?

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

In a throttling process (Joule-Thomson expansion), for an ideal gas:

The correct answer is C: Temperature remains constant. For ideal gas, enthalpy H depends only on temperature. In throttling (isenthalpic process), H = constant, so T = constant for ideal gas. For real gases, T may change based on Joule-Thomson coefficient.

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Difficulty: All Easy Medium Hard 231–240 of 247

Topics in Chemical Engineering

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

Q.231 Medium Mass Transfer

A spray tower is used for absorption where droplets fall through a rising gas stream. The interfacial area in such a system primarily depends on:

A Droplet size and number of droplets

B Tower height only

C Gas flow rate only

D Pressure and temperature

Correct Answer: A. Droplet size and number of droplets

EXPLANATION

Interfacial area 'a' in spray towers is directly proportional to the total surface area of droplets, which depends on droplet size (smaller droplets = larger area) and droplet density.

Test

Q.232 Medium Mass Transfer

In a wetted wall column for gas absorption, the liquid film thickness (δ) affects the mass transfer rate. Increasing δ will:

A Increase the mass transfer rate

B Decrease the mass transfer rate

C Have no effect on the mass transfer rate

D Create turbulence and increase mass transfer

Correct Answer: B. Decrease the mass transfer rate

EXPLANATION

The liquid phase mass transfer coefficient k_L is inversely related to film thickness: k_L = D_AB/δ. Increasing δ decreases k_L and hence the mass transfer rate.

Test

Q.233 Medium Mass Transfer

The mass transfer rate from a solid sphere dissolving in a flowing liquid can be described using the Ranz-Marshall correlation. Which parameter is NOT included in this correlation?

A Reynolds number

B Schmidt number

C Froude number

D Sherwood number

Correct Answer: C. Froude number

EXPLANATION

The Ranz-Marshall correlation for a sphere is Sh = 2 + 0.6 Re^(1/2) Sc^(1/3). Froude number (related to gravity effects) is not part of this correlation.

Test

Q.234 Medium Mass Transfer

A stripping operation is being designed to remove dissolved CO₂ from water using air. The mass transfer is primarily limited by:

A The gas phase resistance

B The liquid phase resistance

C The interfacial resistance

D The membrane resistance

Correct Answer: B. The liquid phase resistance

EXPLANATION

For CO₂-air-water system, CO₂ has low solubility in water, making the liquid phase the controlling resistance in mass transfer.

Test

Q.235 Medium Mass Transfer

In a membrane separation process, the Sherwood number (Sh) for mass transfer at the membrane surface is defined as:

A Sh = k_L * L / D_AB

B Sh = k_G * P / D_AB

C Sh = k_m * R_m / D_AB

D Both A and B depending on phase

Correct Answer: D. Both A and B depending on phase

EXPLANATION

Sherwood number is defined differently for liquid (Sh = k_L * L / D_AB) and gas phases (Sh = k_G * R_g * T / (P * D_AB)), depending on the system.

Test

Q.236 Medium Mass Transfer

In a distillation column, the interface equilibrium at the liquid-vapor boundary can be described by:

A Raoult's Law only

B Henry's Law only

C Either Raoult's Law or Henry's Law depending on the system

D Dalton's Law

Correct Answer: C. Either Raoult's Law or Henry's Law depending on the system

EXPLANATION

Raoult's Law applies to ideal solutions (high concentration), while Henry's Law applies to dilute solutions. The choice depends on the system behavior.

Test

Q.237 Medium Mass Transfer

Which correlation is commonly used for mass transfer in turbulent pipe flow?

A Gnielinski correlation

B Ranz-Marshall correlation

C Chilton-Colburn analogy

D Both A and C

Correct Answer: D. Both A and C

EXPLANATION

Both Gnielinski correlation (modified form) and Chilton-Colburn analogy (j_D = j_H = j_f/2) are applicable for turbulent pipe flow mass transfer.

Test

Q.238 Medium Mass Transfer

Which of the following equations is used to calculate the mass transfer coefficient in laminar flow over a flat plate?

A Sh = 0.664 Re^(1/2) Sc^(1/3)

B Sh = 0.037 Re^(4/5) Sc^(1/3)

C Sh = 4.0 + 1.86(ReSc)^(1/3)

D Sh = 2 + 0.6 Re^(1/2) Sc^(1/3)

Correct Answer: A. Sh = 0.664 Re^(1/2) Sc^(1/3)

EXPLANATION

The Ranz-Marshall correlation for laminar flow over a flat plate is Sh = 0.664 Re^(1/2) Sc^(1/3), derived from boundary layer theory.

Test

Q.239 Medium Mass Transfer

In a cocurrent absorption tower where gas and liquid flow in the same direction, compared to counter-current operation:

A Cocurrent towers require larger height for same separation

B Cocurrent towers are more efficient

C Both achieve similar efficiency with same contact time

D Cocurrent is preferred for high solubility gases

Correct Answer: A. Cocurrent towers require larger height for same separation

EXPLANATION

Counter-current flow provides greater concentration differences throughout the tower (larger average driving force), requiring less height and contact time compared to cocurrent operation for equivalent separation.

Test

Q.240 Medium Mass Transfer

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

A Temperature

B Pressure

C Composition (mole fractions x_A, x_B)

D Molecular weights of components

Correct Answer: C. Composition (mole fractions x_A, x_B)

EXPLANATION

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).

Test

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