Transmission Of Heat Question 28
Question: Two identical square rods of metal are welded end to end as shown in figure (i), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (ii), the same amount of heat will flow through the rods in
[NCERT 1982]
Options:
A) 1 minute
B) 2 minutes
C) 4 minutes
D) 16 minutes
Show Answer
Answer:
Correct Answer: A
Solution:
$ T=\frac{K _{1}{\theta _{1}}+K _{2}{\theta _{2}}}{K _{1}+K _{2}} $
$ =\frac{300\times 100+200\times 0}{300+200}=60{}^\circ C $ (R = Thermal resistance)
Therefore $ ( \frac{Q}{t} )=\frac{k\pi r^{2}({\theta _{1}}-{\theta _{2}})}{L}\propto \frac{r^{2}}{L} $ ($ \frac{Q _{1}}{Q _{2}}={{( \frac{r _{1}}{r _{2}} )}^{2}}( \frac{l _{2}}{l _{1}} )={{( \frac{1}{2} )}^{2}}\times ( \frac{2}{1} )=\frac{1}{2} $ Q and $ Q _{2}=2Q _{1} $ are same)
Therefore $ \frac{Q}{t}=\frac{KA\Delta \theta }{l} $
Therefore $ 6000=\frac{200\times 0.75\times \Delta \theta }{1} $ (Series resistance $ \Delta \theta =\frac{6000\times 1}{200\times 0.75}=40{}^\circ C $ and parallel resistance $ \frac{K _{A}A({\theta _{1}}-\theta )}{l}=\frac{K _{B}A(\theta -{\theta _{2}})}{l} $ )
BETA
