A steel pipe 8.25 m long is installed at 45°C. Find the decrease in length when coolants at -60°C pass through the pipe
Coefficient expansion for copper in Celsius
1.7*10^-5/C°
Correction, for steel
1.3*10^-5/C°
That's 1.3E-5 WHAT/C. meters, cm, ? Substitute into the following:
delta L = alpha*delta T*L
You can read more about it here.
http://en.wikipedia.org/wiki/Thermal_expansion
So would this be the setup?
(1.3x10^-5/C°)(8.25m)(-105°C)=-0.01m
To find the decrease in length of the steel pipe, we need to use the coefficient of linear expansion. The coefficient of linear expansion for steel is typically given as 11.7 x 10^-6 per °C.
First, convert the temperatures from Celsius to Kelvin. Kelvin temperature is obtained by adding 273.15 to the Celsius temperature.
The initial temperature of the pipe, T1 = 45°C + 273.15 = 318.15 K.
The final temperature of the pipe, T2 = -60°C + 273.15 = 213.15 K.
Next, calculate the change in temperature (ΔT) by subtracting the initial temperature (T1) from the final temperature (T2):
ΔT = T2 - T1 = 213.15 K - 318.15 K = -105 K.
Now, we can use the formula for the change in length (ΔL) of a material:
ΔL = α * L0 * ΔT,
where α is the coefficient of linear expansion, L0 is the initial length of the pipe, and ΔT is the change in temperature.
Substituting the values:
α = 11.7 x 10^-6 per °C,
L0 = 8.25 m,
ΔT = -105 K.
ΔL = (11.7 x 10^-6 per °C) * (8.25 m) * (-105 K).
Calculating the result:
ΔL = -0.01021 m.
Therefore, the decrease in length of the steel pipe when coolants at -60°C pass through it is approximately 0.01021 m.