A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0^(@)C. What is the change in the diameter of the hole when the sheet is heated to 227^(@)C ? Coefficient of linear expansion of copper =1.70xx10^(-5)K^(-1).

A hole is drilled in a copper sheet. The diameter of the hole is 4.24

1.	A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0^(@)C. What is the change in the diameter of the hole when the sheet is heated to 227^(@)C ? Coefficient of linear expansion of copper =1.70xx10^(-5)K^(-1).
Answer» Solution :But area of hole is `A_(1)` at TEMPERATURE `T_(1)=27+273=300K` `:.A_(1)=(pid_(1)^(2))/(4)=(pixx(4.24)^(2))/(4)` `:.A_(1)=4.4944pi" cm"^(2)` Area of hole becomes `A_(2)` at temperature `T_(2)=227+273=500K`. `:.A_(2)=A_(1)(1+beta Delta T)` `(pid_(2)^(2))/(4)=4.4944pi[1+2alpha(T_(2)-T_(1))]" where "beta=2alpha` `:.d_(2)^(2)=4xx4.4944[1+2xx1.7xx10^(-5)XX(500-300)]` `:.d_(2)^(2)=4xx4.944[1+2xx1.7xx10^(-5)xx200]` `:.d_(2)^(2)=4xx4.944[1+0.0068]` `:.d_(2)^(2)=4xx4.944xx1.0068` `d_(2)^(2)=18.0998~~18` `:.d_(2)=sqrt(18.1)=4.2544" cm"` `:.` Change in diameter of hole `Deltad=d_(2)-d_(1)` `=4.2544-4.2400` `=0.0144" cm"` `=1.44xx10^(-2)" cm"`