Fourier’s law MCQs With Answer

Fourier’s law MCQs With Answer

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Fourier’s law MCQs With Answer provides B. Pharm students a focused review of heat conduction fundamentals applied to pharmaceutical processes. This SEO-friendly introduction covers key terms like Fourier’s law, heat flux, thermal conductivity, thermal diffusivity, steady and transient conduction, and practical links to tablet coating, drying, sterilization, and lyophilization. The concise, exam-oriented questions and answers reinforce concepts such as one-dimensional conduction, thermal resistance, boundary conditions, and temperature gradients, helping pharmacy undergraduates master heat transfer essentials for lab work and exams. Keywords included: Fourier’s law, heat conduction, thermal conductivity, B. Pharm, heat transfer, MCQs, pharmaceutical processing. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the vector form of Fourier’s law for heat conduction?

  • q = -k ∇T
  • q = k ∇T
  • q = -ρ c ∇T
  • q = h (T – T∞)

Correct Answer: q = -k ∇T

Q2. What is the one-dimensional form of Fourier’s law along x-direction?

  • qx = -k (dT/dx)
  • qx = k (dT/dx)
  • qx = -k (d2T/dx2)
  • qx = ρ c (dT/dt)

Correct Answer: qx = -k (dT/dx)

Q3. What are the SI units of thermal conductivity k?

  • W/m·K
  • W/m^2
  • J/kg·K
  • m^2/s

Correct Answer: W/m·K

Q4. What are the SI units of heat flux q (magnitude of heat flow per area)?

  • W/m^2
  • W/m·K
  • J/kg
  • K/W

Correct Answer: W/m^2

Q5. According to Fourier’s law, heat flows in which direction relative to the temperature gradient?

  • From high to low temperature, opposite to ∇T
  • From low to high temperature, same as ∇T
  • Perpendicular to ∇T
  • Independent of ∇T

Correct Answer: From high to low temperature, opposite to ∇T

Q6. Which property controls the rate of heat conduction in a material?

  • Thermal conductivity
  • Electrical resistivity
  • Specific surface area
  • Porosity only

Correct Answer: Thermal conductivity

Q7. Thermal diffusivity α is defined as:

  • α = k / (ρ c)
  • α = ρ c / k
  • α = k · ρ · c
  • α = k / L

Correct Answer: α = k / (ρ c)

Q8. The Fourier number (Fo) used in transient heat conduction is given by:

  • Fo = α t / L^2
  • Fo = k t / (ρ c)
  • Fo = q / (k ΔT)
  • Fo = h L / k

Correct Answer: Fo = α t / L^2

Q9. Which phenomenon is directly described by Fourier’s law?

  • Heat conduction
  • Convection mixing
  • Electromagnetic radiation
  • Mass diffusion

Correct Answer: Heat conduction

Q10. In pharmaceutical tablet coating, Fourier’s law helps to analyze:

  • Heat conduction into tablet cores during drying
  • Chemical reaction kinetics only
  • Particle size distribution
  • pH variation in coat solvents

Correct Answer: Heat conduction into tablet cores during drying

Q11. For a homogeneous plane wall under steady one-dimensional conduction with constant k, the temperature profile is:

  • Linear with position
  • Exponential with position
  • Logarithmic with position
  • Quadratic with position

Correct Answer: Linear with position

Q12. Thermal resistance for conduction through a plane slab of area A and thickness L is:

  • R = L / (k A)
  • R = k A / L
  • R = 1 / (h A)
  • R = L^2 / k

Correct Answer: R = L / (k A)

Q13. Which of these is a correct analogy between heat and mass transfer?

  • Fourier’s law (heat) is analogous to Fick’s law (mass)
  • Fourier’s law is analogous to Raoult’s law
  • Convection is analogous to Fick’s law
  • Radiation is analogous to diffusion

Correct Answer: Fourier’s law (heat) is analogous to Fick’s law (mass)

Q14. Thermal conductivity of most metals compared to polymers is generally:

  • Much higher
  • Much lower
  • About the same
  • Irrelevant to heat flow

Correct Answer: Much higher

Q15. In anisotropic materials, thermal conductivity is represented as:

  • A tensor
  • A scalar constant
  • Always zero
  • Independent of direction

Correct Answer: A tensor

Q16. Which boundary condition prescribes the heat flux at a surface?

  • Neumann boundary condition
  • Dirichlet boundary condition
  • Robin boundary condition
  • Periodic boundary condition

Correct Answer: Neumann boundary condition

Q17. A convective boundary at a surface couples Fourier’s law with which relation?

  • Newton’s law of cooling q = h (Ts – T∞)
  • Fick’s law for mass flux
  • Stefan-Boltzmann radiation law only
  • Hooke’s law for stress

Correct Answer: Newton’s law of cooling q = h (Ts – T∞)

Q18. The transient one-dimensional heat equation in a homogeneous material is:

  • ∂T/∂t = α ∂^2T/∂x^2
  • ∂T/∂x = α ∂^2T/∂t^2
  • q = -k ∂^2T/∂x^2
  • ∂^2T/∂t^2 = α ∂T/∂x

Correct Answer: ∂T/∂t = α ∂^2T/∂x^2

Q19. Thermal contact resistance at an interface increases when:

  • Surface roughness and gaps increase
  • Materials are perfectly bonded
  • Contact pressure becomes very high
  • Surfaces are metallurgically fused

Correct Answer: Surface roughness and gaps increase

Q20. For cylindrical steady radial conduction through a hollow cylinder, the thermal resistance depends on:

  • ln(r2/r1) term
  • Linear r2 − r1 only
  • r2^2 − r1^2 only
  • Inverse of ln(r2/r1)

Correct Answer: ln(r2/r1) term

Q21. Effective thermal conductivity of a porous wet pharmaceutical tablet usually:

  • Increases with moisture content
  • Decreases with moisture content
  • Does not change with moisture
  • Becomes infinite

Correct Answer: Increases with moisture content

Q22. Which method is commonly used to measure thermal conductivity in lab for powders or small samples?

  • Hot-wire method
  • Chromatography
  • Spectrophotometry
  • Mass spectrometry

Correct Answer: Hot-wire method

Q23. If thermal conductivity k is doubled while ΔT and geometry remain same, what happens to steady heat flux?

  • Heat flux doubles
  • Heat flux halves
  • Heat flux unchanged
  • Heat flux becomes zero

Correct Answer: Heat flux doubles

Q24. Which non-Fourier effect becomes important at very short time scales or nanoscale?

  • Ballistic transport (Cattaneo–Vernotte or non-Fourier behavior)
  • Classical Fourier conduction always applies
  • Convective dominance only
  • Steady-state conduction only

Correct Answer: Ballistic transport (Cattaneo–Vernotte or non-Fourier behavior)

Q25. The temperature gradient unit in SI is:

  • K/m
  • W/m^2
  • W/m·K
  • J/kg·K

Correct Answer: K/m

Q26. Which expression gives the magnitude of heat flux for one-dimensional conduction through slab?

  • q = k (ΔT / L)
  • q = k L / ΔT
  • q = ΔT / (k L)
  • q = ρ c ΔT

Correct Answer: q = k (ΔT / L)

Q27. In a composite wall with layers in series, overall thermal resistance is:

  • Sum of individual resistances
  • Product of individual resistances
  • Inverse of sum of conductances only for parallel
  • Always equal to the largest single resistance

Correct Answer: Sum of individual resistances

Q28. Which parameter primarily affects heat penetration time into a solid?

  • Thermal diffusivity α
  • Electrical conductivity
  • Surface color only
  • Solubility

Correct Answer: Thermal diffusivity α

Q29. The unit of thermal diffusivity α in SI is:

  • m^2/s
  • W/m·K
  • kg/m^3
  • J/kg

Correct Answer: m^2/s

Q30. In steady-state conduction, the term ∂T/∂t equals:

  • Zero
  • One
  • Infinity
  • α

Correct Answer: Zero

Q31. Which is an appropriate use of Fourier’s law in pharmaceutical engineering?

  • Modeling heat transfer in dryer trays and tablet cores
  • Predicting chemical reaction stoichiometry
  • Estimating tablet dissolution pH only
  • Measuring microbial load

Correct Answer: Modeling heat transfer in dryer trays and tablet cores

Q32. For a slab with perfect insulation on one face and constant temperature on the other, the insulated face has which boundary condition?

  • Zero heat flux (Neumann with q = 0)
  • Constant temperature (Dirichlet)
  • Convective flux with h > 0
  • Periodic boundary condition

Correct Answer: Zero heat flux (Neumann with q = 0)

Q33. Which term represents heat generation per unit volume in the heat equation?

  • q”’ (volumetric heat generation)
  • h (convective coefficient)
  • k (thermal conductivity)
  • ρ (density)

Correct Answer: q”’ (volumetric heat generation)

Q34. In finite difference discretization of Fourier’s law, the central difference approximates the derivative as:

  • (T_{i+1} − T_{i−1}) / (2 Δx)
  • (T_{i+1} − T_i) / Δx only
  • (T_i − T_{i−1}) / Δx only
  • Second derivative approximate (T_{i+1} − 2T_i + T_{i−1}) / Δx^2

Correct Answer: (T_{i+1} − T_{i−1}) / (2 Δx)

Q35. Which heat transfer mode is NOT described by Fourier’s law?

  • Radiation between surfaces
  • Conduction within solids
  • Steady conduction in fluids at rest
  • One-dimensional conduction

Correct Answer: Radiation between surfaces

Q36. In heat conduction through a plane wall, doubling the thickness L (with same k and ΔT) results in:

  • Half the heat flux
  • Double the heat flux
  • No change in heat flux
  • Zero heat flux

Correct Answer: Half the heat flux

Q37. Overall heat transfer coefficient U for a wall with convection on both sides relates to resistances as:

  • 1/U = 1/h1 + L/k + 1/h2 (per unit area)
  • U = h1 + h2 + k/L
  • U = k / L only
  • U = h1 h2 / k

Correct Answer: 1/U = 1/h1 + L/k + 1/h2 (per unit area)

Q38. Which is a correct practical implication of low thermal conductivity in a drug formulation?

  • Slower internal heat penetration during drying or sterilization
  • Faster heat penetration always
  • No effect on drying time
  • Instant temperature uniformity

Correct Answer: Slower internal heat penetration during drying or sterilization

Q39. The magnitude of heat flux q equals k times:

  • The magnitude of temperature gradient |∇T|
  • The temperature squared
  • The density times temperature
  • The thermal resistance

Correct Answer: The magnitude of temperature gradient |∇T|

Q40. In modeling lyophilization (freeze-drying), Fourier’s law is used to estimate:

  • Heat conduction through frozen cake affecting sublimation rate
  • Vapor pressure of solvent only
  • Chemical degradation kinetics exclusively
  • Particle size enlargement

Correct Answer: Heat conduction through frozen cake affecting sublimation rate

Q41. Which equation expresses conservation of energy leading to the heat equation?

  • ρ c ∂T/∂t = ∇·(k ∇T) + q”’
  • ρ ∂u/∂t = ∇·(k ∇u) only
  • ∇×E = −∂B/∂t
  • F = m a

Correct Answer: ρ c ∂T/∂t = ∇·(k ∇T) + q”’

Q42. Which factor does NOT directly affect thermal conductivity of a pharmaceutical solid?

  • Color of the solid (unless correlated with composition)
  • Porosity
  • Moisture content
  • Crystal structure

Correct Answer: Color of the solid (unless correlated with composition)

Q43. For radial conduction in a long cylinder under steady-state, temperature profile is:

  • Logarithmic with radius
  • Linear with r
  • Quadratic with r
  • Independent of r

Correct Answer: Logarithmic with radius

Q44. Which of the following best describes “effective thermal conductivity” in composite or porous media?

  • A homogenized property accounting for multiple phases and voids
  • A microscopic measure only for single crystal
  • Always equal to the highest constituent conductivity
  • Independent of microstructure

Correct Answer: A homogenized property accounting for multiple phases and voids

Q45. Numerical stability of explicit finite difference scheme for transient conduction often requires:

  • Fo ≤ 0.5 (time step restriction related to Fo)
  • No restriction on time step
  • Very large time steps for accuracy
  • Negative time steps

Correct Answer: Fo ≤ 0.5 (time step restriction related to Fo)

Q46. In pharmaceutical sterilization by moist heat, Fourier’s law helps quantify:

  • Temperature penetration into product to ensure microbial kill
  • Antibiotic potency only
  • Moisture uptake unrelated to heat
  • pH changes exclusively

Correct Answer: Temperature penetration into product to ensure microbial kill

Q47. The sign in Fourier’s law q = -k ∇T indicates:

  • Heat flows from higher to lower temperature
  • Heat flows from lower to higher temperature
  • There is no physical meaning
  • Heat flows perpendicular to gradient

Correct Answer: Heat flows from higher to lower temperature

Q48. Thermal resistance unit in SI is:

  • K/W
  • W/m^2
  • W/m·K
  • m^2/s

Correct Answer: K/W

Q49. Which statement about steady vs transient conduction is true?

  • Steady-state has no time dependence; transient changes with time
  • Transient has no spatial variation
  • Steady-state always means uniform temperature
  • Transient implies zero heat flux

Correct Answer: Steady-state has no time dependence; transient changes with time

Q50. To estimate thermal conductivity experimentally from temperature vs time data, one typically:

  • Solves inverse conduction problem using measured boundary/temperature histories
  • Directly reads k from thermometer color
  • Uses Fourier number equal to one always
  • Assumes zero heat flux everywhere

Correct Answer: Solves inverse conduction problem using measured boundary/temperature histories

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