Question

The densities of wood and benzene at $0^{\circ }C$ are $880kg/m^3$ and $900kg/m^3$ respectively. The coefficients of volume expansion are $1.2\times {10}^{-3}{/}^{\circ }C$ for wood and $1.5\times {10}^{-3}{/}^{\circ }C$ for benzene. At what temperature will a piece of wood just sink in benzene?

• A. ${73}^{\circ }C$.
• B. ${83}^{\circ }C$.
• C. ${42}^{\circ }C$.
• D. ${120}^{\circ }C$.

Answer 1

The correct option is B ${83}^{\circ }C$.

The wood will just sink in the benzene when densities of both are equal,

i.e., ${\rho }_1={\rho }_2$.

Now, as density is inversely proportional to volume, $\rho ={\rho }_o/(1+\gamma \theta )$

where $\gamma$ is coefficient of volume expansion and $\theta$ is the change in temperature.

Let change in temperature for obtaining equal densities be $\theta$.

so from given values, $\frac{880}{1+1.2\times {10}^{-3}\times \theta }=\frac{900}{1+1.5\times {10}^{-3}\times \theta }$

$\Rightarrow \theta ={83}^{o}C$

So final temperature at which wood would just get sink is $0^o+\theta ={83}^{o}C$