Properties Of Solids And Liquids Question 445
Question: Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is$ 100{}^\circ C $ , then the temperature difference between the ends of other diagonal will be (where / is the length of each rod)
Options:
A) $ 0{}^\circ C $
B) $ \frac{100}{l}{}^\circ C $
C) $ \frac{100}{2l}{}^\circ C $
D) $ 100{}^\circ C $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Suppose temperature difference between A and B is $ 100{}^\circ C $ and $ {\theta _{\Alpha }} > {\theta _{B}} $
Heat current will flow from A to B via path ACB and ADB. Since all therod are identical, so,$ {{(\Delta \theta )} _{Ac}}={{(\Delta \theta )} _{AD}} $
(Because heat current $ H=\frac{\Delta \theta }{R}; $
here R = same for all) $ \Rightarrow {\theta _{A}}-{\theta _{C}}={\theta _{A}}-{\theta _{D}}\Rightarrow {\theta _{C}}={\theta _{D}} $ i.e., temperature difference between C and D will be zero.
