Question

The coefficient of volume expansion of a liquid is $49 \times 10^{-5}\, K ^{-1}$. When temperature is raised by $30^{\circ} C$, then which of the following statement is correct?

• A. Its density decreases.
• B. Its density increases.
• C. Its fractional decrease in density is $2.5 \times 10^{-2}$.
• D. Its fractional increase in density is $2.5 \times 10^{-2}$.

Answer 1

Answer: (A)

Variation of density with temperature is given by
$\rho^{\prime}=\frac{\rho}{1+\alpha_{V} \Delta \theta}$
where, $\rho=$ density at given temperature
and $\rho^{\prime}=$ density at unknown temperature.
So, its density decreases with temperature.
Fractional decrease is
$\frac{\rho^{\prime}-\rho}{\rho}=\left(\frac{1}{1+49 \times 10^{-5} \times 30}-1\right)=1.5 \times 10^{-2}$
Thus, the statement given in option is correct, rest are incorrect.