Thermal Properties of Matter

Question : 8

Total: 22

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 =1.70×10–5K–1.

Solution:

Here, Coefficient of linear expansion of copper, α=1.70×10–5K–1
ΔT=227–27=200°C
Therefore, coefficient of superficial expansion of copper
β=2α=2×1.70×10–5K–1
β=3.40×10–5K–1
Area of hole at 27°C,
S1=

πD12

(4.24)2 cm2
=π×4.4944cm2
If D2 cm is the diameter of the hole at 227°C, then Area of the hole at 227°C,
S2=

πD22

cm2
Increase in area =S2−S1=S1βΔT

S2=S1+S1βΔT
⇒S2=S1(1+βΔT)

πD22

=π×4.4944×(1+3.4×10−5(227−27))
D22=(4.24)2×(1.0068)
⇒D2=4.2544cm
Change in diameter =D2−D1
=4.2544−4.24
=0.0144 cm

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