Question

The coefficient of volume expansion of a material is \(5 \times 10^{-4}\ ^\circ \text{C}^{-1}\). The fractional change in its density for a \(40^\circ\text{C}\) rise in temperature is nearly

• A. 0.01
• B. 0.02
• C. 0.03
• D. 0.04

Hint:

For small temperature changes, fractional density change is directly calculated using \( \frac{\Delta \rho}{\rho} = -\gamma \Delta T \).

Answer 1

The Correct Option is B

Density \( \rho \) is inversely proportional to volume \( V \). When volume increases due to heating, density decreases: \[ \frac{\Delta \rho}{\rho} \approx -\gamma \Delta T \] Where: \[ \gamma = 5 \times 10^{-4}\ ^\circ \text{C}^{-1}, \quad \Delta T = 40^\circ\text{C} \] \[ \Rightarrow \frac{\Delta \rho}{\rho} = -5 \times 10^{-4} \times 40 = -0.02 \] Hence, the magnitude of fractional change in density is approximately \(0.02\).