ધારો કે એક પ્રવાહી બુંદનું બાષ્પીભવન થતા તેની સપાટી ઊર્જામાં ઘટાડો થાય છે કે,જેથી તેનું તાપમાન અચળ રહે છે.આ શકય બને તે માટે બુંદની લઘુતમ ત્રિજયા કેટલી હશે? પ્રવાહીનું પૃષ્ઠતાણ \(=\) \(T\) , પ્રવાહીની ઘનતા \(=\) \(\rho \) અને પ્રવાહીની બાષ્પયન ગલનગુપ્ત ઊર્જા \(L\) છે.

A \(\frac{{2T}}{{\rho L}}\;\)
B \(\;\frac{{\rho L}}{T}\)
C \(\sqrt {\;\frac{T}{{\rho L}}} \)
D \(\;\frac{T}{{\rho L}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{{2T}}{{\rho L}}\;\)

Step-by-step Solution

Detailed explanation

When radius is decrease by \(\Delta R,\) \(4\pi {R^2}\Delta R\rho L = 4\pi T\left[ {{R^2} - {{\left( {R - \Delta R} \right)}^2}} \right]\) \( \Rightarrow \rho {R^2}\Delta RL = T\left[ {{R^2} - {R^2} + 2R\Delta R - \Delta {R^2}} \right]\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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