Question

The coefficient of volume expansion of glycerine is $ 49 \times 10^{-5} \, \text{K}^{-1} $. The percentage change in its density for a $ 50^\circ \text{C} $ rise in temperature is

• A. 3.54
• B. 5.24
• C. 4.25
• D. 2.45

Hint:

For volume expansion problems, remember that the fractional change in volume is given by \( \frac{\Delta V}{V} = \beta \Delta T \), and the density changes oppositely since volume and density are inversely related.

Answer 1

The Correct Option is D

We are given: - The coefficient of volume expansion of glycerine: \( \beta = 49 \times 10^{-5} \, \text{K}^{-1} \), - Temperature rise: \( \Delta T = 50^\circ \text{C} \). The volume expansion coefficient \( \beta \) is defined as the fractional change in volume per unit temperature change: \[ \frac{\Delta V}{V} = \beta \Delta T \] This is the change in volume per unit volume. Since density \( \rho \) is inversely proportional to volume, the fractional change in density is: \[ \frac{\Delta \rho}{\rho} = - \beta \Delta T \]
Thus, the percentage change in density is: \[ % \, \Delta \rho = - \beta \Delta T \times 100 \] Substitute the given values: \[ % \, \Delta \rho = - (49 \times 10^{-5}) \times 50 \times 100 \] \[ % \, \Delta \rho = - 2.45 \]
Thus, the percentage change in density is \( 2.45% \).