Answer to Question #262982 in Physics for ibrahim Jibril

Question

A hole of cross-sectional area 100 c m 2 is cut in a piece of steel at 20 o C . What is the area of the hole if the steel is heated from 20 o C to 100 o C ? The coefficient of linear expansion of steel is 1.10 × 10 − 5 o C

Answer 1

We can find the area of the hole if the steel is heated from $20^{\circ}C$ to $100^{\circ}C$ as follows:

$$\Delta A=2\alpha A_0\Delta T,$$ $$A-A_0=2\alpha A_0\Delta T,$$ $$A=A_0(1+2\alpha\Delta T),$$ $$A=100\ cm^2\times(1+2\times1.10\times10^{-5}\ (^{\circ}C)^{-1}\times80^{\circ}C),$$ $$A=100.2\ cm^2.$$