We know that rate of heat flowH=kAlT1-T2Temeprature difference across first, second and third rods are T1-ϕ1, ϕ1-ϕ2 and ϕ2-T2GivenH1=H2=H3⇒k1AT1-ϕ1l1=k2Aϕ1-ϕ2l2=k3Aϕ2-T2l3Comparing with ⇒k1AT1-ϕ1l1=k2Aϕ1-ϕ2l2=k3AA-Bl3we haveA=ϕ2B=T2

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W e k n o w t h a t r a t e o f h e a t f l o w H = \frac{k A}{l} (T_{1} - T_{2}) T e m e p r a t u r e d i f f e r e n c e a c r o s s f i r s t, s e c o n d a n d t h i r d r o d s a r e (T_{1} - ϕ_{1}), (ϕ_{1} - ϕ_{2}) a n d (ϕ_{2} - T_{2}) G i v e n H_{1} = H_{2} = H_{3} \Rightarrow \frac{k_{1} A (T_{1} - ϕ_{1})}{l_{1}} = \frac{k_{2} A (ϕ_{1} - ϕ_{2})}{l_{2}} = \frac{k_{3} A (ϕ_{2} - T_{2})}{l_{3}} C o m p a r i n g w i t h \Rightarrow \frac{k_{1} A (T_{1} - ϕ_{1})}{l_{1}} = \frac{k_{2} A (ϕ_{1} - ϕ_{2})}{l_{2}} = \frac{k_{3} A (A - B)}{l_{3}} w e h a v e A = ϕ_{2} B = T_{2}

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