Question

Determine the change in volume of a block of a cast iron 5cm x 10cm x 6cm, when the temperature changes from 15°C to 47°C. The coefficient of linear expansion of the cast iron is
0.000 010°C^-1.

Answer 1

We can find the change in volume of a block of a cast iron from the formula:

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

here, $V=300\ cm^3$ is the volume of the block of the cast iron, $\Delta V$ is the change in volume of the block of the cast iron, $\alpha_V=3\alpha_L$ is the volume thermal expansion coefficient of the cast iron, $\alpha_L=1.0\cdot10^{-5}\ ^{\circ}C^{-1}$ is the linear thermal expansion coefficient of the cast iron and $\Delta T=47\ ^{\circ}C-15\ ^{\circ}C=32\ ^{\circ}C$ is the change in temperature.

Then, from this formula we can calculate $\Delta V$:

$$\Delta V=3\alpha_LV\Delta T,$$ $$\Delta V=3\cdot 1.0\cdot10^{-5}\ ^{\circ}C^{-1}\cdot 300\ cm^3\cdot 32\ ^{\circ}C=0.29\ cm^3.$$

Answer:

$\Delta V=0.29\ cm^3.$