Question

Match List-I with List-II.

List-I (Theory Proposed/Characteristic)	List-II (Thinker/Name of Theory, etc.)
(A) Saturated flow in soil	(I) Wien's law
(B) Soil textural analysis	(II) Darcy's law
(C) Wavelength of emitted radiation–temperature relation	(III) Fick's law
(D) Diffusive flux of gas	(IV) Stokes law

Choose the correct answer from the options given below.

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

Hint:

Remember the core transport equations:
- Water flow $\rightarrow$ Darcy's Law
- Particle settling $\rightarrow$ Stokes' Law
- Gas diffusion $\rightarrow$ Fick's Law

Answer 1

The Correct Option is C

Step 1: Understanding the Concept: 
Soil physics and environmental biophysics use several mathematical laws to describe the transport of water, air, sediment, and thermal radiation. 

Step 2: Detailed Explanation: 
Let us match the concepts in List-I with their physical laws in List-II: 
- (A) Saturated flow in soil $\rightarrow$ (II) Darcy's law: Darcy's law states that the rate of fluid flow through a porous medium is proportional to the hydraulic gradient: \[ q = -K_{sat} \frac{dH}{dx} \] 
- (B) Soil textural analysis $\rightarrow$ (IV) Stokes law: Textural analysis by sedimentation (pipette or hydrometer method) uses Stokes' law, which relates the settling velocity of spherical particles to their radius: \[ v = \frac{2}{9} \frac{g (\rho_s - \rho_w) r^2}{\eta} \] 
- (C) Wavelength of emitted radiation-temperature relation $\rightarrow$ (I) Wien's law: Wien's displacement law states that the wavelength of peak emission ($\lambda_{max}$) from a blackbody is inversely proportional to its absolute temperature ($T$): \[ \lambda_{max} T = b \] 
- (D) Diffusive flux of gas $\rightarrow$ (III) Fick's law: Fick's first law describes gas diffusion through soil pores along a concentration gradient: \[ J = -D \frac{dC}{dx} \] 
This gives the combination: (A)-(II), (B)-(IV), (C)-(I), (D)-(III). 

Step 3: Final Answer: 
The matching matches Option (C).