SATHEE: Properties Of Solids And Liquids Question 114

Properties Of Solids And Liquids Question 114

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 $l_{1}$ and $l_{2}$ 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) $\frac{l_{1} - l_{2}}{l_{1} t_{1} - l_{2} t_{2}}$

C) $\frac{l_{1} + l_{2}}{l_{2} t_{1} + l_{1} t_{2}}$

D) $\frac{l_{1} + l_{2}}{l_{1} t_{1} + l_{2} t_{2}}$

Show Answer

Answer:

Correct Answer: A

Solution:

Suppose, height of liquid in each arm before rising the temperature is l.

With temperature rise height of liquid in each arm increases i.e. l1 > l and l2 > l

Also $l = \frac{l_{1}}{1 + γ t_{1}} = \frac{l_{2}}{1 + γ t_{2}}$

therefore $l_{1} + γ l_{1} t_{2} = l_{2} + γ l_{2} t_{1}$

therefore $γ = \frac{l_{1} - l_{2}}{l_{2} t_{1} - l_{1} t_{2}}$

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Properties Of Solids And Liquids Question 114

Question: In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures t1 and t2 . The liquid columns in the two arms have heights l1 and l2 respectively. The coefficient of volume expansion of the liquid is equal to

Options:

Answer:

Solution:

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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 $l_{1}$ and $l_{2}$ respectively. The coefficient of volume expansion of the liquid is equal to