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Physics-

General

Easy

Question

In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures $t subscript 1 end subscript$ and $t subscript 2 end subscript.$ The liquid columns in the two arms have heights $l subscript 1 end subscript$ and $l subscript 2 end subscript$ respectively. The coefficient of volume expansion of the liquid is equal to

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

The correct answer is: $fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction$

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

With temperature rise height of liquid in each arm increases $i. e. blank l subscript 1 end subscript greater than l blank a n d blank l subscript 2 end subscript greater than l$
Also $l equals fraction numerator l subscript 1 end subscript over denominator 1 plus gamma t subscript 1 end subscript end fraction equals fraction numerator l subscript 2 end subscript over denominator 1 plus gamma t subscript 2 end subscript end fraction$
$rightwards double arrow l subscript 1 end subscript plus gamma l subscript 1 end subscript t subscript 2 end subscript equals l subscript 2 end subscript plus gamma l subscript 2 end subscript t subscript 1 end subscript rightwards double arrow gamma equals fraction numerator l subscript 1 end subscript minus l subscript 2 end subscript over denominator l subscript 2 end subscript t subscript 1 end subscript minus l subscript 1 end subscript t subscript 2 end subscript end fraction$

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