A brass of length 100m increases to 100.5m, when heated from 50 to calculate it linear expansivity
Linear expansivity (α) is a measure of how much a material expands per unit length when heated.
The equation for linear expansivity is given by:
ΔL = α * L * ΔT
Where:
ΔL = change in length
α = linear expansivity
L = initial length
ΔT = change in temperature
Given:
Initial length (L) = 100 m
Final length (L + ΔL) = 100.5 m
Change in temperature (ΔT) = 50 °C
Substituting the values into the equation, we can solve for α:
ΔL = α * L * ΔT
100.5 m - 100 m = α * 100 m * 50 °C
0.5 m = 5000 α
Simplifying the equation, we find:
α = 0.5 m / 5000
α = 0.0001 m/°C
Therefore, the linear expansivity of the brass is 0.0001 m/°C.
To calculate the linear expansivity of brass, we can use the equation:
ΔL = α * L * ΔT
Where:
ΔL is the change in length of the brass
α is the linear expansivity coefficient of brass
L is the initial length of the brass
ΔT is the change in temperature
Given:
Initial length (L) = 100 m
Change in length (ΔL) = 100.5 m - 100 m = 0.5 m
Change in temperature (ΔT) = 50 °C
We need to rearrange the equation to solve for α:
α = ΔL / (L * ΔT)
Substituting the given values:
α = 0.5 m / (100 m * 50 °C)
Simplifying:
α = 0.5 m / 5000 m °C
Finally, the linear expansivity (α) of brass is:
α = 0.0001 °C^(-1)
Therefore, the linear expansivity of brass is 0.0001 °C^(-1).