Answer to Question #119996 in Mechanics | Relativity for Samson

Question

A square sheat of steal has a side of 15cm at 00 C. Determine its area at 400C. (Linear expansivity of steel = 1.1x10-5 0C-1

Answer 1

Length of the square plate is at $T_i=0^{\circ}C$ is $L_0=15cm = 0.15m$ ,thus $A_0=L_0^2=0.0225m^2$ ,$T_f=400^{\circ}C$

$\alpha_L=1.1\times 10^{-5}K^{-1}$ .

Let,$A$ the required area and $\Delta T=T_f-T_i=400K$ .

We know that ,

$$A=A_0(1+2\alpha_L \Delta T)$$

Thus on plugin the values in above equation we get,

$$A=0.0225(1+2\times 1.1\times 10^{-5} \times400)\\ \implies A=0.022698m^2$$