The linear expansivity of a material is the fractional increase in its length per degree Celsius. Given a temperature change ΔT, the new length L after heating is related to the initial length L₀ by the formula:
L = L₀ (1 + αΔT)
where α is the linear expansivity.
In this case, the initial side length of the square plate is L₀ = 10 cm, the linear expansivity is α = 2 × 10⁻⁵ /K, and the temperature change is ΔT = 100°C - 30°C = 70°C.
We can plug these values into the formula to find the length of the plate after heating:
L = 10 cm × (1 + 2 × 10⁻⁵ /K × 70 K) = 10 cm × (1 + 0.0014) = 10 cm × 1.0014 = 10.014 cm
The new area A of the square plate will be the square of the new length:
A = L² = (10.014 cm)² ≈ 100.28 cm²
So, the area of one face of the plate will increase to approximately 100.28 cm² after heating.
A square plate of sides 10 cm is made of a metal of linear expansivity
2
×
10
-
5
/K. As the plate is heated from 30°C to 100°C, the area of one face of the plate will increase to
1 answer