Answer to Question #136761 in Physics for Lovelife

Question

Calculate the increase in volume when 1500cm3 of steel is heated from 0°c to 40°c take coefficient of linear expansivity as [1.2x10^-5 °c^-1]

Answer 1

We can find the increase in volume from the formula:

$$\dfrac{\Delta V}{V} = \alpha_V \Delta T,$$

here, $\Delta V$ is the increase in volume, $V = 1500 \ cm^3$ is the volume of the steel, $\alpha_V = 3 \alpha_L$ is the coefficient of volume expansivity, $\alpha_L = 1.2 \cdot 10^{-5} \ ^{\circ}C^{-1}$ is the coefficient of linear expansivity and $\Delta T$ is the temperature change.

Then, from this formula we can calculate the increase in volume:

$$\Delta V = 3\alpha_L V \Delta T,$$ $$\Delta V = 3 \cdot 1.2 \cdot 10^{-5} \ ^{\circ}C^{-1} \cdot 1500 \ cm^3 \cdot 40 \ ^{\circ}C^{-1} = 2.16 \ cm^3,$$ $$\Delta V =2.16 \ cm^3 \cdot (\dfrac{1 \ m}{100 \ cm})^3 = 2.16 \cdot 10^{-6} \ m^3.$$

Answer:

$\Delta V = 2.16 \ cm^3 = 2.16 \cdot 10^{-6} \ m^3.$