A metal rod 80 cm long increased in length by 0.09 cm when the temperature was raised by 93.6 degrees determine the liner expansitivity of metal
To determine the linear expansivity of the metal, we can use the equation:
ΔL = α * L * ΔT
Where:
ΔL = change in length of the rod
α = linear expansivity of the metal
L = original length of the rod
ΔT = change in temperature
We are given:
ΔL = 0.09 cm
L = 80 cm
ΔT = 93.6 °C
Substituting these values into the equation, we have:
0.09 cm = α * 80 cm * 93.6 °C
Simplifying, we get:
0.09 cm = α * 7488 cm °C
Solving for α, we divide both sides of the equation by 7488 cm °C:
α = 0.09 cm / 7488 cm °C
α ≈ 0.000012 cm/°C
Therefore, the linear expansivity of the metal is approximately 0.000012 cm/°C.
To determine the linear expansivity of the metal, we can use the formula:
ΔL = (α)(L)(ΔT)
Where:
ΔL is the change in length of the rod
α is the linear expansivity of the metal
L is the initial length of the rod
ΔT is the change in temperature
Given:
ΔL = 0.09 cm
L = 80 cm
ΔT = 93.6 degrees
Rearranging the formula, we can solve for α:
α = ΔL / (L * ΔT)
Plugging in the values, we have:
α = 0.09 cm / (80 cm * 93.6 degrees)
Calculating this:
α ≈ 0.000120428 cm/degrees
Therefore, the linear expansivity of the metal is approximately 0.000120428 cm/degrees.