A steel wire, 150 m long at 10°C, has a coefficient of linear expansion of 11 ´ 10-6/C°. Give its change in length as the temperature changes from 10°C to 45°C.
To calculate the change in length of the steel wire as the temperature changes, we can use the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the initial length of the steel wire
α is the coefficient of linear expansion
ΔT is the change in temperature
Given:
L = 150 m
α = 11 × 10^(-6) / °C
ΔT = 45°C - 10°C = 35°C
Let's substitute these values into the formula:
ΔL = 150 m * 11 × 10^(-6) / °C * 35°C
Simplifying:
ΔL = 0.0000165 m * 35
ΔL = 0.0005775 m
Therefore, the change in length of the steel wire as the temperature changes from 10°C to 45°C is approximately 0.0005775 meters.
To find the change in length of the steel wire as the temperature changes, we can use the formula for linear expansion:
ΔL = αLΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length
ΔT is the change in temperature
Given:
Coefficient of linear expansion, α = 11 × 10^(-6) / °C
Original length, L = 150 m
Change in temperature, ΔT = 45 °C - 10 °C = 35 °C
Substituting these values into the formula, we can calculate the change in length:
ΔL = (11 × 10^(-6)/°C) × (150 m) × (35 °C)
First, we calculate the product of the coefficient of linear expansion and the original length:
(11 × 10^(-6)/°C) × (150 m) = 1.65 × 10^(-3) m/°C
Now we multiply this by the change in temperature:
(1.65 × 10^(-3) m/°C) × (35 °C) = 0.05775 m
The change in length of the steel wire as the temperature changes from 10°C to 45°C is approximately 0.05775 meters.
Delta L = 11*10^-6 * (45 - 10)
= 385*10^-6 = 3.85*10^-4 Meters.