When a bottle is heated from $t_{1}^{0} C$ to $t_{2}^{0} C$ , x gram of liquid is expelled and m gram of liquid remained.Then the coefficient of real expansion is

\frac{x}{m (t_{2} - t_{1})}

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\frac{x}{m (t_{2} - t_{1})} + 3 α

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\frac{x}{m (t_{2} - t_{1})} - 3 α

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\frac{m}{x (t_{2} - t_{1})} - 3 α

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Solution

The correct option is B $\frac{x}{m (t_{2} - t_{1})} + 3 α$
For apparent expanstion, $m γ_{a} (t_{2} - t_{1}) = x$
Apparent coefficient of expansion would be given as $\frac{m a s s e x p e l l e d}{m a s s r e m a i n e d \times c h a n g e i n t e m p e r a t u r e}$
$⟹ γ_{a} = \frac{x}{m (t_{2} - t_{1})}$
This is the coefficient of expansion as seen by the remaining mass.
But to an observer outside, $γ_{r e a l} = γ_{a} + γ_{g} = \frac{x}{m (t_{2} - t_{1})} + 3 α$

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