Properties Of Solids And Liquids Question 409
Question: In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures $ t _{1} $ and $ t _{2} $ . The liquid columns in the two arms have heights $ l _{2} $ respectively. The coefficient of volume expansion of the liquid is equal to
Options:
A) $ \frac{l _{1}-l _{2}}{l _{2}t _{1}-l _{1}t _{2}} $
B) $ \frac{l _{1}-l _{2}}{l _{1}t _{1}-l _{1}t _{1}} $
C) $ \frac{l _{1}-l _{2}}{l _{2}t _{1}-l _{1}t _{2}} $
D) $ \frac{l _{1}-l _{2}}{l _{1}t _{1}-l _{1}t _{1}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Suppose, height of liquid in each arm before With temperature rise height of liquid in each With the temperature rise height of liquid in each arm increases i.e $ l _{1}>l $ and $ l _{2}>l $ Also $ l=\frac{l _{1}}{1+\gamma t _{1}}=\frac{l _{2}}{1+\gamma t _{2}} $
$ \Rightarrow l _{1}+\gamma l _{2}t _{2}=l _{2}+\gamma l _{2}t _{1}\Rightarrow \gamma =\frac{l _{1}-l _{2}}{l _{2}t _{1}-l _{1}t _{2}} $
