A solid whose volume does not change with temperature floats in a liquid. For tw

Question

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures

t_{1}

and

t_{2}

of the liquid, fractions

f_{1}

and

f_{2}

of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

Options:

A . f1−f2f2t1−f1t2

B . f1−f2f1t1−f2t2

C . f1+f2f2t1+f1t2

D . f1+f2f1t1+f2t2

Answer: Option A
:
A
As with the rise in temperature, the liquid undergoes volume expansion therefore the fraction of solid submerged in liquid increases.
Fraction of solid submerged at

{t_{1}}^{\circ} C = f_{1}

= Volume of displaced liquid

= V_{0} (1 + γ t_{1}) \dots \dots (i)

and fraction of solid submerged at

{t_{2}}^{\circ} C = f_{2}

= Volume of displaced liquid

= V_{0} (1 + γ t_{2}) \dots \dots (i i)

From (i) and (ii)

\frac{f_{1}}{f_{2}} = \frac{1 + γ t_{1}}{1 + γ t_{2}}

\Rightarrow

γ = \frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}

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