Professor $\mathfrak{X}$ and his experiments! -1

Classical Mechanics Level 3

Professor $\mathfrak{X}$ is a very ingenious scientist and researcher.

Once Professor $\mathfrak{X}$ was doing some experiments in his laboratory related to heat and thermal expansion. He took a metal ball and heated it until its temperature increased by $30\ ^{\circ}\text{C}.$ Then he found that the volume of the metal ball increased by $0.18\%$ .

Assuming isotropic behavior of the metal ball, calculate the coefficient of linear expansion of the metal and help Professor $\mathfrak{X}$ in his research.

The answer is 0.00002.

1 solution

Nelvson Shine
May 11, 2014

For a solid, we can ignore the effects of pressure on the material, and the volumetric thermal expansion coefficient can be written :

$\frac{\Delta V}{V * \Delta T}$ = $\alpha_V$

since $\Delta V =$ $\frac{0.18}{100}$ V or $\frac{18}{10000} V$ , $\Delta T = 30$ , and $\alpha_V = 3 \alpha_L$ then

$\frac{\Delta V}{V * \Delta T}$ = $3\alpha_L$

$\frac{\Delta V}{V * \Delta T*3}$ = $\alpha_L$

$\frac{ \frac{18}{10000} V }{V * \Delta T*3}$ = $\alpha_L$

$\alpha_L$ = $\frac{18}{10000*3*30}$

$\alpha_L$ = $0.00002$

Thus the answer is $0.00002$ or 2e-5

Same method here!

Maharnab Mitra - 7 years, 1 month ago

Professor X \mathfrak{X} X and his experiments! -1

The answer is 0.00002.

1 solution

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Professor $\mathfrak{X}$ and his experiments! -1