Final answer:
The change in the area of a square hole in a sheet of copper caused by a temperature increase of 23K is approximately 0.032 cm², by applying the coefficient of linear expansion for copper.
Step-by-step explanation:
To calculate the change in the area of the square hole in the copper sheet with a temperature increase, we need to apply the principles of thermal expansion. The coefficient of linear expansion (α) for copper is given as 1.7 × 10⁻µ (°C)⁻¹. Since area expansion is involved, the change in each dimension due to temperature is effectively doubled, leading to the area changing by a factor of the linear expansion coefficient times two.
The original area (A1) of the square hole is:
- A1 = side × side = 5.3 cm × 5.3 cm = 28.09 cm²
The change in length (ΔL) of a side due to thermal expansion is calculated by ΔL = αLΔT, where:
- α = 1.7 × 10⁻µ (°C)⁻¹ (coefficient of linear expansion)
- L = original length of the side (5.3 cm)
- ΔT = change in temperature (23 K or °C)
Substituting the values, we get:
ΔL = 1.7 × 10⁻µ × 5.3 cm × 23 = 0.0020889 cm per side.
The new length of each side is:
L + ΔL = 5.3 cm + 0.0020889 cm = 5.3020889 cm
The new area (A2) of the square hole is:
A2 = (5.3020889 cm)² = approximately 28.122 cm²
The change in the area (ΔA) of the hole is:
ΔA = A2 - A1 = approximately 28.122 cm² - 28.09 cm² = approximately 0.032 cm²
So, the change in the area of the square hole when the temperature of the copper sheet is increased by 23 K is approximately 0.032 cm².