Discussion Forum



1)

Two conducting cyclinders of equal length but different radii are connected in series between two heat  baths kept at temperatures  T1= 300K and T2=100K, as shown in the figure. The radius of the bigger cyclinder is twice that of the smaller one and the thermal conductivites of the materials of the smaller and the larger cyclinders are K1 and K2 , respectively . If the temperature at the junction of the cyclinders in the steady state is 200K, then K1/K2=  .........

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A) 3

B) 4

C) 2

D) 5

Answer:

Option B

Explanation:

Rate of heat flow will be same.

$\therefore$   $\frac{300-200}{R_{1}}=\frac{200-100}{R_{2}} $         

                                                                      ( as  $H= \frac{\text{d}Q}{\text{d}t}=\frac{T.D}{R}$)

 $\therefore$          $R_{1}=R_{2}\Rightarrow \frac{L_{1}}{K_{1}A_{1}}=\frac{L_{2}}{K_{2}A_{2}}$

$\Rightarrow$         $\frac{K_{1}}{K_{2}}=\frac{A_{2}}{A_{1}}=4$