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Avogadro's Law & Gay Lussac's Law

In a vertical...

Question

In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures $t_{1} a n d t_{2}$ . The liquid columns in the two arms have heights $l_{1} a n d l_{2}$ respectively. The coefficient of volume expansion of the liquid is equal to

A

\frac{l_{1} - l_{2}}{l_{2} t_{1} - l_{1} t_{2}}

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B

\frac{l_{1} - l_{2}}{l_{1} t_{1} - l_{2} t_{2}}

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C

\frac{l_{1} + l_{2}}{l_{2} t_{1} + l_{1} t_{2}}

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D

\frac{l_{1} + l_{2}}{l_{1} t_{1} + l_{2} t_{2}}

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Solution

The correct option is A $\frac{l_{1} - l_{2}}{l_{2} t_{1} - l_{1} t_{2}}$
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. $l_{1} > l a n d l_{2} > l$
$A l s o l = \frac{l_{1}}{1 + γ t_{1}} = \frac{l_{2}}{1 + γ t_{2}} \Rightarrow l_{1} + γ l_{1} t_{2} = l_{2} + γ l_{2} t_{1} \Rightarrow γ = \frac{l_{1} - l_{2}}{l_{2} t_{1} - l_{1} t_{2}}$

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