Question

Match the transport processes in Column I with the relationships in Column II.
Column I
(P) Molecular momentum transport
(Q) Molecular mass transport
(R) Molecular energy transport
(S) Radiation energy transport
Column II
(1) Stefan-Boltzmann law
(2) Newton's law of viscosity
(3) Fick's law
(4) Fourier law

• A. P – 2, Q – 3, R – 4, S – 1
• B. P – 4, Q – 3, R – 2, S – 1
• C. P – 3, Q – 1, R – 4, S – 2
• D. P – 2, Q – 1, R – 4, S – 3

Hint:

These are the three fundamental laws of transport phenomena, often taught together due to their analogous mathematical form (Flux = -Constant \(\times\) Gradient). - {Momentum:} Newton's Law - {Energy (Conduction):} Fourier's Law - {Mass:} Fick's Law Radiation (Stefan-Boltzmann) is a different mode of heat transfer and doesn't follow the same gradient form.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question requires matching different types of transport phenomena with the fundamental physical law that governs them. Transport phenomena deal with the movement of momentum, energy, and mass.
Step 2: Detailed Matching:
- (P) Molecular momentum transport: The transport of momentum in a fluid due to a velocity gradient is described by viscosity. The relationship between shear stress (\(\tau\), which is momentum flux) and the velocity gradient (\(du/dy\)) is given by Newton's law of viscosity (\(\tau = \mu \frac{du}{dy}\)). P matches with 2.
- (Q) Molecular mass transport: The diffusion of a chemical species due to a concentration gradient is described by Fick's first law. The mass flux (\(J\)) is proportional to the concentration gradient (\(dC/dx\)), with the proportionality constant being the diffusion coefficient (\(J = -D \frac{dC}{dx}\)). Q matches with 3.
- (R) Molecular energy transport (conduction): The transport of heat energy through a medium due to a temperature gradient is described by Fourier's law of heat conduction. The heat flux (\(q\)) is proportional to the temperature gradient (\(dT/dx\)), with the proportionality constant being the thermal conductivity (\(q = -k \frac{dT}{dx}\)). R matches with 4.
- (S) Radiation energy transport: The transport of energy via electromagnetic waves emitted by a body due to its temperature is described by laws of thermal radiation. The total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature (\(E = \sigma T^4\)). This is the Stefan-Boltzmann law. S matches with 1.
The correct matching is: P-2, Q-3, R-4, S-1. This corresponds to option (A).
Step 4: Why This is Correct:
Each pairing correctly links a specific transport mechanism to its governing physical law. Option (A) contains all the correct pairings.