બે પદાર્થ જેની ઉષ્મા વાહકતા \(3K\) અને \(K\) અને જાડાઈ \(d\) અને \(3d\) છે તેને આકૃતિમાં દર્શાવ્યા પ્રમાણે જોડેલ છે.બહારની સપાટીના તાપમાન અનુક્રમે \(\theta_2\) અને \(\theta_1\) છે.\(\left( {\theta _2} > {\theta _1} \right) \) તો જંકશનનું તાપમાન કેટલું હશે?

A \(\frac{{{\theta \,}_2 + {\theta \,}_1}}{2}\)
B \(\frac{\theta _1}{10} + \frac{9\theta _2}{10}\)
C \(\frac{\theta_1}{3} + \frac{2\theta_2}{3}\)
D \(\frac{\theta _1}{6} + \frac{5\theta _2}{6}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\theta _1}{10} + \frac{9\theta _2}{10}\)

Step-by-step Solution

Detailed explanation

At steady state: \({\left( {\frac{{\Delta q}}{{\Delta t}}} \right)_1} = {\left( {\frac{{\Delta q}}{{\Delta t}}} \right)_2}\) \(\frac{{3mkA\left( {{\theta _2} - \theta } \right)}}{d} = \frac{{kA\left( {\theta - {\theta _1}} \right)}}{{3d}}\)…

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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