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

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$\frac{h_{1} - h_{2}}{h_{2} T_{1} - h_{1} T_{2}}$

$\frac{h_{1} - h_{2}}{h_{1} T_{1} - h_{2} T_{2}}$

$\frac{h_{1} + h_{2}}{h_{2} T_{1} - h_{1} T_{2}}$

$\frac{h_{1} + h_{2}}{h_{2} T_{1} + h_{1} T_{2}}$

answer is A.

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Detailed Solution

$\begin{array}{l} Let the height of liquid in the columns is h when they are at same temperature. \\ with rise temperature heights of liquid columns also increase \\ h = \frac{h_{1}}{1 + {γT}_{1}} = \frac{h_{2}}{1 + {γT}_{2}} \\ h_{1} + {γh}_{1} T_{2} = h_{2} + {γh}_{2} T_{1} \\ γ = \frac{h_{1} - h_{2}}{h_{2} T_{1} - h_{1} T_{2}} \end{array}$