Question

The active element of a certain laser is made Glas rod 30cm long And 1.50cm in diameter. What will be the increase in it volume if the temperature of the rod is increase 70.0degree

Answer 1

The increase in it volume is given by the following expression:

$$\Delta V = \alpha_V\cdot V\cdot \Delta T$$

where $\alpha_V = 25.5\times 10^{-6}K^{-1}$ is the volumetric thermal expansion coefficient of glass, $V$ is the initial volume and $\Delta T = 70\degree C = 70K$ is the  increase of temperature. The initial volume of the rode is:

$$V = \dfrac{\pi d^2L}{4}$$

which is the volume of a cylinder with a diameter $d = 1.5cm = 0.015m$ and length $L = 30cm = 0.3m$. Substituting the expression for the volume into the first equation, obtain:

$$\Delta V = \alpha_V\cdot \dfrac{\pi d^2L}{4}\cdot \Delta T \\ \Delta V = 25.5\times 10^{-6}\cdot \dfrac{\pi\cdot 0.30\cdot 015^2\cdot }{4}\cdot 70 \approx 9.46\times 10^{-8}m^3$$

Answer. $9.46\times 10^{-8}m^3$.