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

Solution.

$L_0=15cm=0.15m;$

$T_0=0^oC;$

$T_1=400^oC;$

$\alpha_L=1.1\sdot10^{-5 }\dfrac{1}{oC}$;

$\alpha_L=\dfrac{1}{L}\dfrac{\Delta L}{\Delta T};\implies$ $\Delta L=\alpha_L\Delta T L;$

$\Delta L=1.1\sdot10^{-5}\dfrac{1}{oC}\sdot400^oC\sdot0.15m=66\sdot10^{-5}m;$

$L=L_0+\Delta L;$

$L=0.15m+0.00066m=0.15066m;$

$S=L^2;$

$S=0.15066m\sdot0.15066m=0.0227m^2;$

Answer:$S=0.0227m^2.$