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AMIE Section B Chemical study materials
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AMIE Section B Chemical practice questions

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Question 1Chemical Engineering Thermodynamics

For an ideal gas, which quantity is zero at all temperatures?

  1. The Joule-Thomson coefficient
  2. The internal energy change on isothermal expansion
  3. The enthalpy change on isothermal expansion Correct answer.
  4. The compressibility factor

Explanation

For an ideal gas, enthalpy depends only on temperature, so an isothermal process produces no change in enthalpy. Internal energy likewise depends only on temperature, but the option describing internal energy change on isothermal expansion is a distractor phrased as a change, and the correct zero-at-all-conditions statement concerns enthalpy change under isothermal conditions.

Question 2Chemical Engineering Thermodynamics

The first law of thermodynamics applied to a closed system undergoing an adiabatic process with no shaft work reduces to which statement?

  1. The change in internal energy equals the heat transferred
  2. The change in enthalpy equals the heat transferred at constant pressure
  3. The change in entropy equals the heat transferred divided by temperature
  4. The change in internal energy equals the negative of the work done by the system Correct answer.

Explanation

For a closed system, ΔU = Q − W. Setting Q = 0 for an adiabatic process gives ΔU = −W, meaning the internal energy change equals the negative of the work done by the system. This is the standard reduction of the first law for an adiabatic, shaft-work-free closed system.

Question 3Chemical Engineering Thermodynamics

Which statement correctly describes the entropy change of the universe for a spontaneous process?

  1. It is zero at equilibrium and positive for a spontaneous change Correct answer.
  2. It is negative for reversible processes
  3. It is always negative
  4. It is always positive regardless of reversibility

Explanation

The second law states that the entropy of the universe increases for any spontaneous process and remains constant at equilibrium. For a reversible process, the change is zero, which is the equilibrium case. A negative value would violate the second law.

Question 4Chemical Engineering Thermodynamics

At the critical point of a pure substance, which statement is true?

  1. The vapor pressure equals atmospheric pressure
  2. The latent heat of vaporization reaches a maximum
  3. The densities of the saturated liquid and vapor are equal Correct answer.
  4. The compressibility factor is exactly one

Explanation

At the critical point, the distinction between liquid and vapor disappears, so the saturated liquid and saturated vapor densities become identical. The latent heat of vaporization goes to zero rather than a maximum. The critical pressure is not generally atmospheric.

Question 5Chemical Engineering Thermodynamics

Which equation of state is a cubic equation that incorporates both the attractive and repulsive forces of molecules through two parameters a and b?

  1. The virial equation truncated at the second term
  2. The ideal gas law
  3. The Redlich-Kwong equation
  4. The van der Waals equation Correct answer.

Explanation

The van der Waals equation is a cubic equation of state that corrects the ideal gas law with parameter a for intermolecular attraction and parameter b for molecular volume (repulsion). It is the classic two-parameter cubic equation.

Question 6Chemical Engineering Thermodynamics

The fugacity of a gas approaches which value as the pressure approaches zero?

  1. Zero
  2. The saturation pressure
  3. Unity
  4. The ideal gas pressure Correct answer.

Explanation

Fugacity is defined so that it approaches the ideal gas behavior at low pressure, meaning f/P → 1 as P → 0. Therefore the fugacity approaches the pressure itself. This makes fugacity a corrected pressure that reduces to pressure in the ideal limit.

Question 7Chemical Engineering Thermodynamics

In a binary mixture, Raoult's law is most appropriate for which component?

  1. The component with the highest volatility
  2. The component at infinite dilution
  3. The solvent in a nearly ideal solution Correct answer.
  4. The solute in a dilute solution

Explanation

Raoult's law applies to the solvent in a nearly ideal solution where the mole fraction is close to one. Henry's law is more appropriate for the solute at high dilution. The two laws are complementary limits of the same mixture.

Question 8Chemical Engineering Thermodynamics

A gas mixture contains 2 mol of nitrogen and 3 mol of oxygen. What is the mole fraction of nitrogen?

  1. 0.60
  2. 0.67
  3. 0.20
  4. 0.40 Correct answer.

Explanation

The mole fraction is the moles of the component divided by the total moles. Here 2 mol divided by 5 mol total equals 0.40. This is the standard definition of mole fraction in a mixture.

Question 9Chemical Engineering Thermodynamics

For an ideal gas, the change in internal energy during an isothermal expansion from volume V1 to V2 is best described as which of the following?

  1. Equal to the work done by the gas
  2. Positive, because heat is absorbed
  3. Zero, because internal energy depends only on temperature Correct answer.
  4. Negative, because the gas does work

Explanation

For an ideal gas, internal energy is a function of temperature only. Since temperature is constant in an isothermal process, the change in internal energy is zero. The work done is balanced entirely by heat absorbed.

Question 10Chemical Engineering Thermodynamics

A system undergoes a reversible isothermal compression at temperature T. Which expression gives the entropy change of the system?

  1. ΔS = nCp ln(T2/T1)
  2. ΔS = nR ln(V2/V1) Correct answer.
  3. ΔS = Q/T
  4. ΔS = W/T

Explanation

For an ideal gas undergoing isothermal compression, the entropy change is ΔS = nR ln(V1/V2), which equals −nR ln(V2/V1) for compression. The option expressed as nR ln(V2/V1) is the standard form giving the entropy change for the volume ratio. For isothermal compression V2 < V1, so the entropy change is negative, consistent with the physical situation.

Question 11Chemical Engineering Thermodynamics

A Carnot engine operates between reservoirs at 600 K and 300 K. What is its thermal efficiency?

  1. 0.25
  2. 1.00
  3. 0.75
  4. 0.50 Correct answer.

Explanation

The Carnot efficiency is given by η = 1 − Tc/Th. Substituting Tc = 300 K and Th = 600 K gives η = 1 − 0.5 = 0.50. This is the maximum possible efficiency for any engine operating between these temperatures.

Question 12Chemical Engineering Thermodynamics

For a real gas, the Joule-Thomson coefficient is positive when which condition holds?

  1. The gas behaves ideally
  2. The gas is below its inversion temperature Correct answer.
  3. The gas is compressed isothermally
  4. The gas is above its inversion temperature

Explanation

A positive Joule-Thomson coefficient means the gas cools on throttling, which occurs below the inversion temperature. Above the inversion temperature, the coefficient is negative and the gas warms on throttling. The inversion temperature is where the coefficient changes sign.

Question 13Chemical Engineering Thermodynamics

The chemical potential of component i in an ideal gas mixture is given by which expression?

  1. μi = μi° + RT ln(xiP) Correct answer.
  2. μi = μi° + RT ln(P)
  3. μi = μi° + RT ln(xi)
  4. μi = μi° + xiP

Explanation

For an ideal gas mixture, the chemical potential depends on the partial pressure of the component, which is xiP. Thus μi = μi° + RT ln(xiP), where μi° is the standard chemical potential. This reflects the logarithmic dependence on partial pressure.

Question 14Chemical Engineering Thermodynamics

Which condition must hold at vapor-liquid equilibrium for a multicomponent system?

  1. The total pressure of each phase must be equal only
  2. The temperature of each phase must be equal only
  3. The chemical potential of each component must be equal in all phases Correct answer.
  4. The mole fractions of each component must be equal in all phases

Explanation

At equilibrium, the chemical potential of each component must be equal in every phase present. This is equivalent to equality of fugacity for each component across phases. Equality of temperature and pressure is also required, but the component-wise condition is the chemical potential equality.

Question 15Chemical Engineering Thermodynamics

A binary mixture has an azeotrope. At the azeotropic point, which statement is true?

  1. The activity coefficients are both unity
  2. The vapor pressure is zero
  3. The mixture behaves as an ideal solution
  4. The vapor and liquid compositions are identical Correct answer.

Explanation

At an azeotrope, the vapor and liquid phases have the same composition, so the mixture boils at constant composition. This occurs because the activity coefficients deviate from unity such that the relative volatility becomes one. The mixture is therefore not ideal at the azeotrope.

Question 16Chemical Engineering Thermodynamics

The residual Gibbs free energy of a real gas is related to which quantity by GR/RT = ln φ?

  1. The compressibility factor
  2. The fugacity coefficient Correct answer.
  3. The osmotic coefficient
  4. The activity coefficient

Explanation

The residual Gibbs free energy relative to the ideal gas state is directly related to the fugacity coefficient through GR/RT = ln φ. This relationship connects the deviation from ideal behavior to the fugacity coefficient. The fugacity coefficient therefore quantifies non-ideality.

Question 17Chemical Engineering Thermodynamics

For an ideal solution, the enthalpy of mixing is which of the following?

  1. Positive
  2. Negative
  3. Zero Correct answer.
  4. Equal to the entropy of mixing

Explanation

An ideal solution is defined as one for which the enthalpy of mixing is zero, meaning no heat is absorbed or released on mixing. The entropy of mixing is positive, but the enthalpy change is zero by definition. This is analogous to ideal gas mixtures.

Question 18Chemical Engineering Thermodynamics

The Clapeyron equation relates the slope of the vapor pressure curve to which quantities?

  1. The activity coefficient and the mole fraction
  2. The heat capacity and the temperature
  3. The heat of vaporization and the change in molar volume Correct answer.
  4. The compressibility factor and the pressure

Explanation

The Clapeyron equation is dP/dT = ΔH/(TΔV), relating the slope of the coexistence curve to the enthalpy of phase change and the change in molar volume. For vaporization, this involves the latent heat and the volume change. The Clausius-Clapeyron equation is an approximation of this result.

Question 19Chemical Engineering Thermodynamics

A gas obeys the van der Waals equation with a = 0.364 Pa·m⁶/mol² and b = 4.27×10⁻⁵ m³/mol. At the critical point, the critical compressibility factor Zc predicted by the van der Waals equation is which value?

  1. 0.27
  2. 0.375 Correct answer.
  3. 1.00
  4. 0.50

Explanation

The van der Waals equation predicts a universal critical compressibility factor of Zc = 3/8 = 0.375. This follows from the critical constants expressed in terms of a and b. Real gases typically have Zc around 0.27, which is lower than the van der Waals prediction.

Question 20Chemical Engineering Thermodynamics

In a throttling process through a porous plug, which quantity remains constant?

  1. Gibbs free energy
  2. Entropy
  3. Internal energy
  4. Enthalpy Correct answer.

Explanation

A throttling process is adiabatic with no work done, so the first law gives ΔH = 0, meaning enthalpy is constant. The process is irreversible, so entropy increases. Internal energy changes because pressure and volume change.

Question 21Chemical Engineering Thermodynamics

Two ideal gases at the same temperature and pressure are mixed adiabatically. The entropy of mixing per mole of mixture is given by which expression for equimolar amounts?

  1. R ln 2 Correct answer.
  2. Zero
  3. −R ln 2
  4. 2R ln 2

Explanation

For mixing equimolar ideal gases, the entropy of mixing per mole of mixture is −R Σ xi ln xi = −R(0.5 ln 0.5 + 0.5 ln 0.5) = R ln 2. This is positive, reflecting the increased disorder on mixing. The result is independent of temperature and pressure for ideal gases.

Question 22Chemical Engineering Thermodynamics

For a binary system at low pressure, the fugacity of component i in the vapor phase is best approximated by which expression?

  1. fiV = φi xi P
  2. fiV = xi P
  3. fiV = yi P Correct answer.
  4. fiV = γi xi P

Explanation

At low pressure, the vapor phase behaves nearly ideally, so the fugacity of component i equals its partial pressure, yiP. The fugacity coefficient approaches unity. Liquid-phase non-ideality is handled separately through activity coefficients.

Question 23Chemical Engineering Thermodynamics

The Maxwell relation derived from the Helmholtz free energy A(T,V) is which of the following?

  1. (∂T/∂P)S = (∂V/∂S)P
  2. (∂S/∂P)T = −(∂V/∂T)P
  3. (∂H/∂P)T = V − T(∂V/∂T)P
  4. (∂S/∂V)T = (∂P/∂T)V Correct answer.

Explanation

From dA = −S dT − P dV, the Maxwell relation is (∂S/∂V)T = (∂P/∂T)V. This follows from equality of mixed second partial derivatives of A. The other options correspond to Maxwell relations from other thermodynamic potentials.

Question 24Chemical Engineering Thermodynamics

In an adiabatic steady-flow compressor with negligible kinetic and potential energy changes, the work required per mole is given by which expression for a reversible process?

  1. Ws = ∫P dV
  2. Ws = −∫V dP Correct answer.
  3. Ws = TΔS
  4. Ws = ΔU

Explanation

For a reversible steady-flow adiabatic compressor, the shaft work per mole is Ws = −∫V dP, obtained from the steady-flow energy balance with ΔH = Q + Ws and Q = 0 combined with dH = T dS + V dP. Since the process is isentropic, dH = V dP, giving Ws = ∫V dP for compression work input. The negative sign convention indicates work done on the system.

Question 25Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

For fully developed laminar flow of an incompressible Newtonian fluid through a circular pipe, how does the volumetric flow rate depend on the pipe diameter when pressure gradient and viscosity are held constant?

  1. It is proportional to the diameter to the fourth power Correct answer.
  2. It is independent of the diameter
  3. It is proportional to the diameter
  4. It is proportional to the diameter squared

Explanation

The Hagen-Poiseuille law gives Q = πD⁴ΔP/(128μL) for laminar pipe flow, so the flow rate scales with the fourth power of diameter. This strong dependence explains why small changes in pipe bore greatly alter capacity.

Question 26Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A fluid element in a steady, incompressible, two-dimensional flow field has velocity components u = 3x and v = -3y. What is the volumetric dilatation rate of the element?

  1. -3 s⁻¹
  2. 6 s⁻¹
  3. 0 s⁻¹ Correct answer.
  4. 3 s⁻¹

Explanation

The dilatation rate is the divergence of velocity, ∂u/∂x + ∂v/∂y = 3 + (-3) = 0. A zero divergence is exactly the statement of incompressibility for this steady field.

Question 27Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

Which dimensionless group represents the ratio of inertial forces to viscous forces in a flowing fluid?

  1. Froude number
  2. Nusselt number
  3. Prandtl number
  4. Reynolds number Correct answer.

Explanation

The Reynolds number Re = ρVD/μ compares inertia to viscous resistance and sets whether flow is laminar or turbulent. The other groups compare different physical effects.

Question 28Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

In steady one-dimensional heat conduction through a plane wall of constant thermal conductivity, the temperature profile is:

  1. Linear in position Correct answer.
  2. Parabolic in position
  3. Logarithmic in position
  4. Exponential in position

Explanation

With no heat generation and constant k, the governing equation reduces to d²T/dx² = 0, whose solution is a straight line. The heat flux is therefore uniform across the wall.

Question 29Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

Fick's first law of diffusion states that the molar flux is proportional to:

  1. The square of the concentration gradient
  2. The concentration itself
  3. The integral of concentration over distance
  4. The negative gradient of concentration Correct answer.

Explanation

Fick's first law is J = -D dC/dx, so flux is driven by and proportional to the concentration gradient, with the minus sign indicating flow down-gradient. The proportionality constant is the diffusion coefficient.

Question 30Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

For steady laminar flow through a long circular pipe, the velocity profile across the cross-section is:

  1. Uniform across the radius
  2. Parabolic, with zero velocity at the wall Correct answer.
  3. Linear from centre to wall
  4. Flat in the core with a thin boundary layer

Explanation

The no-slip condition forces zero velocity at the wall while the centreline is a maximum, giving the classic parabolic (Poiseuille) profile. It results from the balance of pressure and viscous forces.

Question 31Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

The thermal conductivity of a material is expressed in which SI units?

  1. W/(m·K) Correct answer.
  2. J/(kg·K)
  3. kg/(m·s)
  4. W/(m²·K)

Explanation

Fourier's law q = -k dT/dx gives k units of W/(m·K), which expresses heat flow per unit length per unit temperature gradient. The other units belong to different transport quantities.

Question 32Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

Which quantity is a measure of the resistance of a fluid to gradual deformation by shear stress?

  1. Vapour pressure
  2. Dynamic viscosity Correct answer.
  3. Surface tension
  4. Bulk modulus

Explanation

Dynamic viscosity μ relates applied shear stress to the resulting rate of shear strain in a Newtonian fluid. It is the fluid's internal resistance to flow.

Question 33Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

Water flows at 2 m/s through a pipe of internal diameter 0.05 m with density 1000 kg/m³ and viscosity 0.001 Pa·s. What is the Reynolds number?

  1. 1000
  2. 100
  3. 100000 Correct answer.
  4. 50000

Explanation

Re = ρVD/μ = (1000 × 2 × 0.05)/0.001 = 100000. This value exceeds the usual laminar-turbulent transition near 2300, so the flow is turbulent.

Question 34Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

For combined conduction and convection from a hot surface to a cold fluid, the Biot number compares:

  1. Inertial forces to viscous forces
  2. Thermal diffusivity to momentum diffusivity
  3. Internal conduction resistance to external convection resistance Correct answer.
  4. Heat capacity to thermal conductivity

Explanation

Bi = hL/k compares the resistance to heat conduction inside a body to the convective resistance at its surface. A small Biot number justifies a lumped-capacitance analysis.

Question 35Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A plane wall 0.1 m thick with thermal conductivity 2 W/(m·K) has faces held at 100 °C and 40 °C. What is the steady heat flux through the wall?

  1. 12 W/m²
  2. 1200 W/m² Correct answer.
  3. 120 W/m²
  4. 12000 W/m²

Explanation

Fourier's law gives q'' = k ΔT/L = 2 × (100 - 40)/0.1 = 1200 W/m². The flux is uniform in steady one-dimensional conduction.

Question 36Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

In fully developed turbulent pipe flow, the mean velocity is approximately 0.82 times the maximum centreline velocity. If the centreline velocity is 5 m/s, what is the approximate mean velocity?

  1. 2.5 m/s
  2. 4.1 m/s Correct answer.
  3. 5.0 m/s
  4. 3.3 m/s

Explanation

Multiplying the centreline velocity by the turbulent velocity-profile factor gives 0.82 × 5 ≈ 4.1 m/s. The flatter turbulent profile makes the mean closer to the maximum than in laminar flow.

Question 37Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

For a laminar boundary layer over a flat plate, the local Nusselt number varies with distance x from the leading edge approximately as:

  1. Proportional to x^0.5 Correct answer.
  2. Proportional to x^0.8
  3. Proportional to x
  4. Independent of x

Explanation

Laminar flat-plate correlations give Nu_x ∝ Re_x^0.5 ∝ x^0.5, so the local heat-transfer coefficient decreases as x^(-0.5). The thermal boundary layer thickens downstream.

Question 38Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A hot sphere of radius 0.05 m at 200 °C is cooled in air at 20 °C with a convective coefficient of 50 W/(m²·K). Using Newton's law of cooling, what is the initial rate of heat loss per unit surface area?

  1. 1800 W/m²
  2. 9000 W/m² Correct answer.
  3. 90 W/m²
  4. 900 W/m²

Explanation

q'' = h(Ts - T∞) = 50 × (200 - 20) = 9000 W/m². The radius is not needed for the flux, only for the total heat rate.

Question 39Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

In steady molecular diffusion of species A through a stagnant, non-diffusing gas B in a tube, the flux of A is described by which relationship?

  1. Stefan diffusion, with flux enhanced by bulk (convective) flow of A Correct answer.
  2. Poiseuille flow of the mixture
  3. Equimolar counter-diffusion, with flux proportional to the gradient alone
  4. Knudsen diffusion, dominated by wall collisions

Explanation

When B is stagnant, the diffusion of A induces a bulk convective flow of the mixture, so the flux is larger than pure Fick diffusion by the factor 1/(1 - yA). This is Stefan diffusion.

Question 40Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

The Prandtl number of a fluid is 0.7. Which statement about the relative thickness of the hydrodynamic and thermal boundary layers in laminar flow is correct?

  1. No thermal boundary layer exists
  2. The two boundary layers have equal thickness
  3. The thermal boundary layer is thinner than the hydrodynamic boundary layer
  4. The hydrodynamic boundary layer is thinner than the thermal boundary layer Correct answer.

Explanation

The ratio δ/δt scales approximately as Pr^(1/3). With Pr = 0.7, this ratio is below unity, so the velocity boundary layer is thinner than the thermal boundary layer.

Question 41Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

For laminar flow in a pipe, the Darcy friction factor f is related to the Reynolds number by:

  1. f = 0.079/Re^0.25
  2. f = 0.316/Re^0.25
  3. f = 16/Re
  4. f = 64/Re Correct answer.

Explanation

The Darcy-Weisbach friction factor for fully developed laminar pipe flow is f = 64/Re. It follows directly from the parabolic velocity profile and the Hagen-Poiseuille result.

Question 42Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A composite wall consists of two layers in series. Layer 1 has resistance R1 = 0.5 K/W and layer 2 has R2 = 1.5 K/W. If the total temperature drop across the wall is 40 K, what is the steady heat-transfer rate?

  1. 20 W Correct answer.
  2. 10 W
  3. 40 W
  4. 80 W

Explanation

Layers in series add their thermal resistances, giving R = 2.0 K/W. The heat rate is Q = ΔT/R = 40/2.0 = 20 W.

Question 43Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

The Schmidt number compares which two quantities?

  1. Heat transfer to mass transfer
  2. Inertial forces to surface tension
  3. Thermal diffusivity to mass diffusivity
  4. Momentum diffusivity to mass diffusivity Correct answer.

Explanation

Sc = ν/D, the ratio of momentum diffusivity (kinematic viscosity) to molecular diffusivity. It plays the same role in mass transfer that the Prandtl number plays in heat transfer.

Question 44Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A fluid flows between two large parallel plates with the lower plate fixed and the upper plate moving at 1 m/s, separated by 0.002 m. If the viscosity is 0.5 Pa·s, what is the shear stress in the fluid?

  1. 25 Pa
  2. 250 Pa Correct answer.
  3. 500 Pa
  4. 0.25 Pa

Explanation

For simple Couette flow the shear stress is τ = μ du/dy = 0.5 × (1/0.002) = 250 Pa. The linear velocity profile makes the gradient uniform.

Question 45Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

The Lewis number of a gas mixture is approximately 1.5. What does this imply about the relative rates of thermal and mass diffusion?

  1. Mass diffusivity exceeds thermal diffusivity
  2. Thermal diffusivity exceeds mass diffusivity Correct answer.
  3. The two diffusivities are equal
  4. No mass diffusion can occur

Explanation

Le = α/D, so a Lewis number of 1.5 means thermal diffusivity is 1.5 times the mass diffusivity. Heat therefore spreads faster than the species in this mixture.

Question 46Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

For steady-state one-dimensional radial conduction through a cylindrical shell of inner radius r1 and outer radius r2, the thermal resistance is:

  1. ln(r2/r1)/(2πkL) Correct answer.
  2. 2πkL/ln(r2/r1)
  3. (r2 - r1)/(2πkL)
  4. (r2 - r1)/(kL)

Explanation

Integrating Fourier's law in cylindrical coordinates gives Q = 2πkL ΔT/ln(r2/r1), so the resistance is ln(r2/r1)/(2πkL). The logarithmic form reflects the growing area with radius.

Question 47Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A fluid flows through a pipe at a Reynolds number of 50000 with a Darcy friction factor of 0.02. For a pipe length of 10 m and diameter 0.1 m, what is the head loss?

  1. Approximately 0.51 m
  2. Approximately 0.051 m
  3. Approximately 51 m
  4. Approximately 5.1 m Correct answer.

Explanation

The Darcy-Weisbach equation gives hf = f (L/D)(V²/2g). Using Re = ρVD/μ with the given values, V ≈ 0.5 m/s, so hf = 0.02 × 100 × 0.25/19.62 ≈ 5.1 m.

Question 48Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

In a boundary-layer flow, the Blasius solution gives a skin-friction coefficient that decreases with distance from the leading edge. Which statement best explains this behaviour?

  1. The fluid viscosity decreases downstream
  2. The Reynolds number decreases downstream
  3. The boundary layer thickens, reducing the wall velocity gradient Correct answer.
  4. The free-stream velocity increases downstream

Explanation

As the laminar boundary layer grows, the velocity gradient at the wall falls, so wall shear stress and skin-friction coefficient decrease. The free-stream velocity and viscosity are constant in the Blasius problem.

Question 49Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

A gas mixture contains species A with a mole fraction of 0.2 at one plane and 0.1 at a plane 0.01 m away. If the diffusivity is 2×10⁻⁵ m²/s and total concentration is 40 mol/m³, what is the approximate Fick's-law molar flux of A?

  1. 4×10⁻³ mol/(m²·s)
  2. 2×10⁻⁵ mol/(m²·s)
  3. 8×10⁻³ mol/(m²·s) Correct answer.
  4. 1.6×10⁻² mol/(m²·s)

Explanation

J = -D (C_A2 - C_A1)/Δx, with concentrations 8 and 4 mol/m³. Thus J = 2×10⁻⁵ × (8 - 4)/0.01 = 8×10⁻³ mol/(m²·s) directed from the higher to the lower concentration.

Question 50Transport Phenomena (Fluid Mechanics, Heat Transfer, Mass Transfer)

Which dimensionless group is used to characterise the regime of flow in a pipe and is defined as the ratio of inertial to viscous forces?

  1. Reynolds number Correct answer.
  2. Prandtl number
  3. Nusselt number
  4. Sherwood number

Explanation

The Reynolds number compares inertial forces to viscous forces and determines whether pipe flow is laminar or turbulent. The other groups compare different transport quantities and do not classify the flow regime.