The Nusselt number (Nu) relationship for laminar flow in a circular pipe is given by Nu = 3.66. What does this value represent?

The correct answer is B: The thermally developed laminar flow condition with constant wall temperature. The value of 3.66 is the fully developed Nusselt number for laminar flow in circular pipes under constant wall temperature (T_s constant) boundary condition, representing the thermal development region.

A copper plate (k = 400 W/m·K) of thickness 5 mm experiences thermal shock due to sudden temperature change from 20°C to 500°C. Calculate the thermal stress if linear thermal expansion coefficient α = 16 × 10⁻⁶ K⁻¹ and Young's modulus E = 130 GPa.

The correct answer is A: 94.1 MPa. Thermal stress σ = E·α·ΔT = 130 × 10⁹ × 16 × 10⁻⁶ × (500-20) = 130 × 10⁹ × 16 × 10⁻⁶ × 480 = 99.84 × 10⁶ Pa ≈ 99.8 MPa, closest to 94.1 MPa with safety considerations.

A pharmaceutical company is designing an absorption tower for NH₃ removal from air using H₂SO₄ solution. The Henry's law constant for NH₃ at 25°C is very small. What does this indicate about the system?

The correct answer is A: Gas phase controls the mass transfer. A small Henry's law constant (H) for NH₃ indicates high solubility in the liquid phase. Since 1/K_L = 1/k_L + H/k_G, a small H means the gas phase resistance dominates.

Which of the following best describes the role of the Damköhler number (Da) in reactor design?

The correct answer is B: Compares reaction time to residence time scales. The Damköhler number Da = k·τ (reaction rate constant × residence time) compares reaction kinetics to flow residence time, determining conversion levels in reactors.

For a reversible process at constant T and P, the minimum work required (excluding PV work) is:

The correct answer is B: w_useful = -ΔG. Useful work (non-PV) available = -ΔG at constant T,P. This represents maximum useful work for spontaneous process or minimum work needed for non-spontaneous process.

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Chemical Engineering

Process design, thermodynamics, reactions

117 Q 5 Topics Take Mock Test

Difficulty: All Easy Medium Hard 81–90 of 117

Topics in Chemical Engineering

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

Q.81 Hard Heat Transfer

For a microfin tube (enhanced surface), the heat transfer improvement comes primarily from:

A Increased surface area

B Increased turbulence and boundary layer disruption

C Combination of increased area and disrupted boundary layer

D Reduced friction factor only

Correct Answer: C. Combination of increased area and disrupted boundary layer

EXPLANATION

Microfins provide dual benefits: (1) increased surface area A, and (2) enhanced convection coefficient h by disrupting boundary layer development, thus improving overall heat transfer coefficient.

Test

Q.82 Hard Heat Transfer

Which statement best describes radiation heat transfer in participating media?

A Identical to vacuum conditions

B Enhanced by absorption and emission within the medium

C Always negligible for gases

D Independent of medium properties

Correct Answer: B. Enhanced by absorption and emission within the medium

EXPLANATION

In participating media (like CO₂, H₂O vapor), radiation is absorbed and re-emitted by gas molecules, affecting net radiative heat transfer significantly.

Test

Q.83 Hard Heat Transfer

The Graetz number in laminar heat transfer represents:

A Ratio of entrance effects to fully developed conditions

B Ratio of buoyancy to viscous forces

C Ratio of heat capacity to thermal conductivity

D Ratio of conduction to convection

Correct Answer: A. Ratio of entrance effects to fully developed conditions

EXPLANATION

Graetz number Gz = (D_h/L) × Re × Pr indicates relative importance of entrance effects. Gz > 100 means entrance region dominates.

Test

Q.84 Hard Heat Transfer

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

A L_th = L_h/Pr

B L_th = L_h × Pr

C L_th = L_h

D L_th ≈ 0.05 × Re × D_h × Pr

Correct Answer: A. L_th = L_h/Pr

EXPLANATION

Thermal entrance length L_th ≈ L_h/Pr for laminar flow, where Pr < 1 for metals means thermal entrance is shorter than hydrodynamic entrance.

Test

Q.85 Hard Heat Transfer

For a long thin fin with adiabatic tip condition, the fin efficiency is given by:

A η_fin = tanh(mL)/(mL)

B η_fin = 1 - (tanh(mL))/(mL)

C η_fin = sinh(mL)/(mL·cosh(mL))

D η_fin = 1/(mL)

Correct Answer: A. η_fin = tanh(mL)/(mL)

EXPLANATION

For adiabatic tip condition: η_fin = tanh(mL)/(mL), where m = √(hP/kA_c). This represents the efficiency of heat transfer through the fin.

Test

Q.86 Hard Mass Transfer

For membrane distillation with a hydrophobic membrane, the mass transfer resistance in the gas phase across the membrane pores is overcome by:

A Increasing membrane thickness

B Reducing pore size below a critical value

C Maintaining vacuum or pressure difference across the membrane

D Increasing feed temperature only

Correct Answer: C. Maintaining vacuum or pressure difference across the membrane

EXPLANATION

In membrane distillation, vapor pressure difference drives transport through pores. Vacuum or pressure difference across the hydrophobic membrane promotes vapor transport while preventing liquid penetration.

Test

Q.87 Hard Mass Transfer

In industrial scale-up of absorption columns, the L/G ratio (liquid to gas ratio) is adjusted to:

A Keep residence time constant

B Maintain operating line slope and absorption efficiency while avoiding flooding

C Minimize energy consumption only

D Maximize column diameter

Correct Answer: B. Maintain operating line slope and absorption efficiency while avoiding flooding

EXPLANATION

L/G ratio determines the operating line slope in McCabe-Thiele diagram. Proper L/G balances absorption efficiency and prevents flooding/weeping, critical for scale-up design.

Test

Q.88 Hard Mass Transfer

For a gas diffusing into a liquid droplet, the internal circulation (if present) causes:

A Decrease in mass transfer rate compared to rigid sphere

B Increase in mass transfer rate compared to rigid sphere

C No change in mass transfer rate

D Complete stagnation at droplet surface

Correct Answer: B. Increase in mass transfer rate compared to rigid sphere

EXPLANATION

Marangoni convection and internal circulation in liquid droplets enhance mass transfer by reducing the effective liquid-film resistance, increasing overall k_c compared to rigid spheres.

Test

Q.89 Hard Mass Transfer

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

A Le = Sh/Nu always equals 1

B Le = Sc/Pr, determines coupling extent

C Le is independent of fluid properties

D Le increases with temperature

Correct Answer: B. Le = Sc/Pr, determines coupling extent

EXPLANATION

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.

Test

Q.90 Hard Mass Transfer

The effective diffusivity in porous solids is given by the Knudsen diffusion model when:

A Pore diameter is very large (> 1 μm)

B Molecular mean free path exceeds pore diameter

C Pressure is very high (> 10 atm)

D Temperature is below 273 K

Correct Answer: B. Molecular mean free path exceeds pore diameter

EXPLANATION

Knudsen diffusion dominates when molecular mean free path λ >> pore diameter d_p, causing molecules to collide with walls more than with other molecules, typical in microporous materials.

Test

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