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

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

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

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

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

answer is A.

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Detailed Solution

Reference temperature is taken at $0 ° C$
$∴ l_{1} = l_{0} ({1 + γ}_{R} (t_{1} -0)) . ...... (1)$

$l_{2} = l_{0} ({1+ γ}_{R} (t_{2} -0)) . ........ (2)$
Eliminating $l_{0}; γ_{R} = \frac{l_{2} - l_{1}}{l_{1} t_{2} - l_{2} t_{1}}$

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