Heat and Thermodynamics 3 Question 27
27. Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T _1=300 K$ and $T _2=100 K$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K _1$ and $K _2$, respectively. If the temperature at the junction of the cylinders in the steady state is $200 K$, then $K _1 / K _2=\ldots \ldots \ldots .$.
(2018 Adv.)
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Answer:
Correct Answer: 27. 4
Solution:
- (d) Rate of heat flow will be same,
$\therefore \frac{300-200}{R _1}=\frac{200-100}{R _2} \quad\left(\right.$ as $\left.H=\frac{d Q}{d t}=\frac{T \cdot D}{R}\right)$
$\therefore \quad R _1=R _2 \Rightarrow \frac{L _1}{K _1 A _1}=\frac{L _2}{K _2 A _2} \Rightarrow \frac{K _1}{K _2}=\frac{A _2}{A _1}=4$
