The length of a steel rod at 5°C is 12.500 m. What is its length when heated to 154°C?
the expansion coefficient is
... α = 1.20E-5 m /m·ºK
ΔL = 1.20E-5 * 12.5 * (154 - 5)
L = 12.500 + ΔL
To find the length of the steel rod when heated to 154°C, we need to consider its coefficient of linear expansion. The coefficient of linear expansion, denoted by α, represents the fractional increase in length per degree Celsius of temperature increase.
The formula to calculate the change in length of an object due to a change in temperature is:
ΔL = α * L * ΔT,
where:
ΔL = change in length,
α = coefficient of linear expansion,
L = original length, and
ΔT = change in temperature.
In this case, we have the initial length (L) of the steel rod at 5°C, which is 12.500 m, and the change in temperature (ΔT) from 5°C to 154°C, which is 154°C - 5°C = 149°C.
However, we still need the coefficient of linear expansion (α) for steel to solve this problem. The coefficient of linear expansion for different materials can vary, so we need to look up the specific value for steel.
Let's assume that the coefficient of linear expansion for steel is α = 12 × 10^(-6) per °C. This is just an example; the actual value may vary.
Now we can substitute the values into the formula:
ΔL = (12 × 10^(-6) per °C) * (12.500 m) * (149°C).
Evaluating the equation gives:
ΔL ≈ 0.01785 m (rounded to five decimal places).
To find the final length of the steel rod (Lf), we add the change in length (ΔL) to the original length (L):
Lf = L + ΔL
= 12.500 m + 0.01785 m
≈ 12.51785 m (rounded to five decimal places).
Therefore, the length of the steel rod when heated to 154°C is approximately 12.51785 meters.