Step 1: Understanding the Concept:
This matching problem tests knowledge across several sub-disciplines of agricultural and process engineering, including heat transfer, thermodynamics of food mixtures, food preservation engineering, and agricultural structural design.
Step 2: Detailed Explanation:
Let us analyze and pair each term individually:
(A) Fouling: This is the accumulation of unwanted material (such as proteins, minerals, or microbial growth) on the solid surfaces of process equipment. It is a major problem inheat exchangers, where it acts as an insulating layer, significantly reducing the heat transfer coefficient. Thus, (A) matches with (II).
(B) Raoult's law: This is a law of physical chemistry stating that the partial vapor pressure of each component of anideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. Thus, (B) matches with (III).
(C) Plank's law (Plank's equation): In food process engineering, Plank's equation is a classical analytical model used to estimate the foodfreezing time. It relates freezing time to the latent heat of fusion, thermal conductivity, temperature differences, and convective heat transfer coefficients. Thus, (C) matches with (IV).
(D) Airy's theory: This is an analytical structural design theory used to estimate the lateral and vertical pressures exerted by bulk grains stored in shallow bins or silos. Unlike deep bins (analyzed by Janssen's equation), shallow bins designed using Airy's theory take into account the wedge-shaped failure plane of the grain mass duringstorage. Thus, (D) matches with (I).
Combining these matches, we obtain: (A)-(II), (B)-(III), (C)-(IV), (D)-(I).
Step 3: Final Answer:
The correct option is (A), representing the match (A)-(II), (B)-(III), (C)-(IV), (D)-(I).