Transmission Of Heat Question 71
Question: The lengths and radii of two rods made of same material are in the ratios 1 : 2 and 2 : 3 respectively. If the temperature difference between the ends for the two rods be the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio
[MP PET 2000]
Options:
A) 1: 3
B) 4 : 3
C) 8 : 9
D) 3 : 2
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{Q}{t}=\frac{KA({\theta _{1}}-{\theta _{2}})}{l} $
Therefore $ \frac{Q}{t}\propto \frac{A}{l}\propto \frac{r^{2}}{l} $ [As $ ({\theta _{1}}-{\theta _{2}}) $ and K are constants]
$ \Rightarrow \frac{{{( \frac{Q}{t} )}_1}}{{{( \frac{Q}{t} )}_2}}$
=$\frac{r _{1}^{2}}{r _{2}^{2}}\times \frac{l _{2}}{l _{1}}=\frac{4}{9}\times \frac{2}{1}=\frac{8}{9} $
BETA
