Transmission Of Heat Question 56
Question: The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio 1 : 2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 $ 4\ cal/\sec $ , that in the shorter rod in $ cal/\sec $ will be
[EAMCET 1986]
Options:
A) 1
B) 2
C) 8
D) 16
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dQ}{dt}=\frac{K(\pi r^{2})d\theta }{dl} $
Therefore $ \frac{{{( \frac{dQ}{dt} )}_s}}{{{( \frac{dQ}{dt} )}_l}}$=
$\frac{K _{s}\times r _{s}^{2}\times l _{l}}{K _{l}\times r _{l}^{2}\times l _{s}} $
= $ \frac{1}{2}\times \frac{1}{4}\times \frac{2}{1} $
Therefore $ {{( \frac{dQ}{dt} )}_s}=\frac{{{( \frac{dQ}{dt} )}_l}}{4}$
=$\frac{4}{4}=1 $
BETA
