Question

Match List I with List II

List I & List II
A. Conduction & I. Stefan-Boltzmann Law
B. Convection & II. Fick's Law
C. Radiation & III. Newton's law of cooling
D. Mass Transfer & IV. Fourier Law

Choose the correct answer from the options given below:

• A. A-II, B-I, C-IV, D-III
• B. A-II, B-IV, C-I, D-III
• C. A-IV, B-III, C-I, D-II
• D. A-IV, B-II, C-I, D-III

Hint:

Associate the modes of transfer with their key physical phenomena to remember the laws:
• Conduction \(\rightarrow\) Gradient in a solid \(\rightarrow\) Fourier's Law
• Convection \(\rightarrow\) Surface to fluid \(\rightarrow\) Newton's Law of Cooling
• Radiation \(\rightarrow\) Electromagnetic waves, \(T^4\) \(\rightarrow\) Stefan-Boltzmann Law
• Mass Transfer \(\rightarrow\) Concentration gradient \(\rightarrow\) Fick's Law

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question requires matching the modes of heat and mass transfer with their corresponding governing laws. We need to identify the fundamental law associated with conduction, convection, radiation, and mass transfer.

Step 2: Detailed Explanation:
Let's analyze each term in List I and find its corresponding law in List II.

• A. Conduction: Heat conduction is the transfer of heat through a stationary medium. The fundamental law governing this process is Fourier's Law of Heat Conduction (\(q = -kA \frac{dT}{dx}\)). This law states that the rate of heat transfer is proportional to the negative temperature gradient and the area. So, A matches with IV.

• B. Convection: Heat convection is the transfer of heat between a surface and a moving fluid. The rate of convective heat transfer is described by Newton's Law of Cooling (\(Q = hA(T_s - T_f)\)). So, B matches with III.

• C. Radiation: Heat radiation is the transfer of energy through electromagnetic waves. The total energy radiated per unit surface area of a black body across all wavelengths per unit time is directly proportional to the fourth power of the black body's thermodynamic temperature. This is described by the Stefan-Boltzmann Law (\(E_b = \sigma T^4\)). So, C matches with I.

• D. Mass Transfer: Mass transfer is the net movement of mass from one location to another. The diffusion of mass is governed by Fick's Law of Diffusion, which states that the molar flux due to diffusion is proportional to the concentration gradient. So, D matches with II.

Step 3: Final Answer:
Based on the matching:
A \(\rightarrow\) IV (Fourier Law)
B \(\rightarrow\) III (Newton's law of cooling)
C \(\rightarrow\) I (Stefan-Boltzmann Law)
D \(\rightarrow\) II (Fick's Law)
This corresponds to the option A-IV, B-III, C-I, D-II.