Question

A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27°C. What is the change in the diameter of the hole when the sheet is heated to 227°C?[ α=1.70×10−5/° C].

A. 1.44×10⁻² cm
B. 1.96×10⁻² cm
C. 1.78×10⁻² cm
D. 1.28×10⁻² cm

Answer 1

The diameter of the hole in the copper sheet increases by 1.44×10⁻⁲ cm when heated from 27°C to 227°C, calculated using the formula for thermal expansion given the linear expansion coefficient.

Step-by-step explanation:

The question is about thermal expansion of materials, specifically how the diameter of a hole in a copper sheet changes when heated from 27°C to 227°C. The linear expansion coefficient (α) for copper is given as 1.70×10⁻⁵/°C. The formula to calculate the change in diameter (ΔD) is ΔD = D₀αΔT, where D₀ is the initial diameter, α is the coefficient of linear expansion, and ΔT is the change in temperature.

First, we calculate the temperature change:

ΔT = 227°C - 27°C = 200°C

Next, we use the formula to find the change in diameter:

ΔD = 4.24 cm × 1.70×10⁻⁵/°C × 200°C = 1.44×10⁻⁲ cm

The change in the diameter of the hole when the sheet is heated to 227°C is 1.44×10⁻⁲ cm, so the correct answer is A. 1.44×10⁻⁲ cm.