The density of steel is 4800kg/m^3 at 20℃. Find the density at 100℃
The density of steel at different temperatures can be calculated using the following formula:
ρt = ρ20 [1 + αt (t - 20)]
Where:
ρt = density of steel at the given temperature (in kg/m^3)
ρ20 = density of steel at 20℃ (in kg/m^3)
αt = coefficient of thermal expansion of steel (in 1/℃)
t = given temperature (in ℃)
The coefficient of thermal expansion of steel is approximately 1.2 × 10^-5 1/℃.
Using the above formula, we can find the density of steel at 100℃.
ρ100 = 4800 [1 + 1.2 × 10^-5 (100 - 20)]
ρ100 = 4986.4 kg/m^3
Therefore, the density of steel at 100℃ is 4986.4 kg/m^3.
To find the density of steel at 100°C, we need to account for the thermal expansion using the coefficient of linear expansion (α) and the initial density (ρ₀).
First, let's calculate the change in temperature (ΔT):
ΔT = 100℃ - 20℃ = 80℃
The coefficient of linear expansion for steel is typically around 12 × 10^-6 /°C.
Next, let's calculate the thermal expansion coefficient (β):
β = α * ΔT = 12 × 10^-6 /°C * 80°C = 0.00096
Now we can find the change in density (Δρ):
Δρ = β * ρ₀ = 0.00096 * 4800 kg/m^3 = 4.608 kg/m^3
Finally, we can find the density at 100℃:
ρ = ρ₀ + Δρ = 4800 kg/m^3 + 4.608 kg/m^3 = 4804.608 kg/m^3
Therefore, the density of steel at 100℃ is approximately 4804.608 kg/m^3.