10-2.Transmission of Heat
normal

$3K, 2K$ અને $K$ ઉષ્મા વાહકતા ધરાવતા સળિયાને આકૃતિમાં દર્શાવ્યા મુજબ ગોઠવેલ છે.જેના છેડાના તાપમાન $100\,^oC, 50\,^oC$ અને $20\,^oC$ તેના જંકશનનું તાપમાન ....... $^oC$ હશે?

A

$60$

B

$70$

C

$50$

D

$35$

Solution

$\frac{{dQ}}{{dt}} = KA\frac{{\Delta T}}{L}$

$For\,the\,first\,rod,\left( {\frac{{dQ}}{{dt}}} \right) = \frac{{3KA}}{L}\left( {100 – \theta } \right)$

$Similarly,{\left( {\frac{{dQ}}{{dt}}} \right)_2} = 2K\frac{A}{L}\left( {\theta  – 50} \right)$

${\left( {\frac{{dQ}}{{dt}}} \right)_3} = K\frac{A}{L}\left( {\theta  – 20} \right)$

$Now,{\left( {\frac{{dQ}}{{dt}}} \right)_1} = {\left( {\frac{{dQ}}{{dt}}} \right)_2} + {\left( {\frac{{dQ}}{{dt}}} \right)_3}$

$ \Rightarrow \,\,3\left( {100 – \theta } \right) = 2\left( {\theta  – 50} \right) + \left( {\theta  – 20} \right)$

$ \Rightarrow \theta  = {70^ \circ }$

Standard 11
Physics

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