Question

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 = 1.70 × 10¯⁵ K–¯¹

Answer 1

At 27   o C, the diameter of the hole is 4.24 cm.

The coefficient of linear expansion of copper is 1.70× 10 −5   K −1

Here, superficial expansion of the copper sheet will be included for solution which is,

β=2α

Area of the hole drilled is,

A 1 = π D 1 2 4 = π× ( 4.24 ) 2 4   cm 2

If D 2 is the diameter of the hole drilled at 227   o C, then area of the hole at 227   o Cis,

A 2 = π D 2 2 4

Coefficient of superficial is,

β=2α =2×1.7× 10 −5 =3.4× 10 −5   o C −1

Change in area is,

A 2 − A 1 = A 1 βΔT A 2 = A 1 [ 1+βΔT ] π D 2 2 4 = π D 1 2 4 [ 1+3.4× 10 −5 ( 227−27 ) ] D 2 2 = ( 4.24 ) 2 [ 1.0068 ] D 2 =4.254 cm

Change in diameter is,

D 2 − D 1 =4.2544−4.24 =0.0144 cm

Hence, the change in the diameter of the hole is 1 .44×10 −2  cm.