Question

If $d_1$ and $d_2$ are the densities of a liquid at $t_1 \,{}^\circ C$ and $t_1 \,{}^\circ C$ then $\frac {d_1}{d_2}$ is (g = coefficient of real expansion)

• A. $\frac{1+\gamma t_1}{1+\gamma t_2}$
• B. $\frac{1-\gamma t_1}{1-\gamma t_2}$
• C. $\frac{1+\gamma t_2}{1+\gamma t_1}$
• D. $\frac{1-\gamma t_2}{1-\gamma t_1}$

Answer 1

Answer: (C)

Let the density of liquid at $0^{\circ} C$ be $d _{0}$.
$
\Longrightarrow d _{1}=\frac{ d _{0}}{1+\gamma t _{1}}
$
Also $d _{2}=\frac{ d _{0}}{1+\gamma t _{2}}$
$
\Longrightarrow \frac{ d _{1}}{ d _{2}}=\frac{1+\gamma t _{2}}{1+\gamma t _{1}}
$