Answer:
1) 5.0066 m
2A) β = 3×10⁻⁷ / °C
2B) 2500.045 cm²
3A) γ = 8.1×10⁻⁵ / °C
3B) 1618.144 cm³
Explanation:
1) Linear thermal expansion is:
ΔL = α L₀ ΔT
where ΔL is the change in length,
α is the linear thermal expansion coefficient,
L₀ is the original length,
and ΔT is the change in temperature.
Given L₀ = 5 m, ΔT = 110°C, and α = 1.2×10⁻⁵ / °C:
ΔL = (1.2×10⁻⁵ / °C) (5 m) (110°C)
ΔL = 0.0066 m
The length increases by , so the new length is:
L = L₀ + ΔL
L = 5 m + 0.0066 m
L = 5.0066 m
2A) The surface expansion coefficient is:
β = 2α
β = 2 (1.5×10⁻⁷ / °C)
β = 3×10⁻⁷ / °C
2B) The change in area is:
ΔA = β A₀ ΔT
ΔA = (3×10⁻⁷ / °C) (50 cm × 50 cm) (60°C)
ΔA = 0.045 cm²
So the new area is:
A = A + ΔA
A = 2500 cm² + 0.045 cm²
A = 2500.045 cm²
3A) The volumetric expansion coefficient is:
γ = 3α
γ = 3 (2.7×10⁻⁵ / °C)
γ = 8.1×10⁻⁵ / °C
3B) The change in volume is:
ΔV = γ V₀ ΔT
ΔV = (8.1×10⁻⁵ / °C) (1600 cm³) (140°C)
ΔV = 18.144 cm³
So the new area is:
V = V + ΔV
V = 1600 cm³ + 18.144 cm³
V = 1618.144 cm³
