Question:hard

Which of the following Law's are based on gradient:
(A) Stefan-Boltzmann law
(B) Fourier's law
(C) Newton's law of cooling
(D) Fick's law

Choose the correct answer from the options given below:

Show Hint

Ask which law depends on temperature to the fourth power instead of on a driving-force gradient or difference.
  • (A), (B) and (C) only.
  • (B), (C) and (D) only.
  • (A), (C) and (D) only.
  • (A), (B) and (D) only.
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Sort the four named laws by what kind of equation each one is.
Step 2: Conduction, Fourier's law, and diffusion, Fick's law, both use a first derivative of a potential, temperature or concentration, with respect to distance, multiplied by a transport coefficient, thermal conductivity or diffusivity. Both are clearly gradient laws.
Step 3: Convective cooling, Newton's law, uses a bulk difference between surface and fluid temperature rather than a derivative, but it is derived from the same underlying idea, heat moves down a temperature gradient inside a thin film near the surface, with the film approximated as a difference divided by film thickness. Because of this shared origin, courses in heat and mass transfer commonly place Newton's law of cooling in the same driving-force family as Fourier's and Fick's laws.
Step 4: Radiative emission, Stefan-Boltzmann law, is fundamentally different in form, tied to \(T^4\) of the emitting surface with no reference to any other point or distance, so no gradient concept is involved at all. It cannot be grouped with the other three.
Step 5: Sorting the four laws this way leaves Fourier's, Newton's and Fick's laws together, with the Stefan-Boltzmann law standing alone outside that group.
\[\boxed{\text{(B), (C) and (D) only}}\]
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