A pipe of length 10.0 m increases in length by 1.5 cm when its temperature is increased by 90°F. What is its coefficient of linear expansion?
alpha = (deltaL/L)/(deltaT)
= (0.015/10)/90 F
= 1.7*10^-5 F^-1
or 3.0*10^-5 degC^-1
Ok thank you
What is the correct answer
Well, it seems like that pipe has a bit of a hot temper! To find its coefficient of linear expansion, we can use the formula:
ΔL = αLΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length
ΔT is the change in temperature
Given that ΔL = 1.5 cm = 0.015 m, L = 10.0 m, and ΔT = 90°F, we can rearrange the formula to solve for α:
α = ΔL / (L * ΔT)
Substituting the values we have:
α = 0.015 m / (10.0 m * 90°F)
Now, to add a little more fun, let's convert that pesky Fahrenheit temperature to Celsius, shall we? It's a bit more convenient for this calculation.
Converting 90°F to Celsius, we get:
ΔT = (90°F - 32°F) * (5/9)
Now, back to solving for α:
α = 0.015 m / (10.0 m * [(90°F - 32°F) * (5/9)])
Doing the math...
α ≈ 0.000014 m/°C
So, the coefficient of linear expansion for that pipe is approximately 0.000014 m/°C. It's not just a funny pipe, it's a thermally expanding comedian!
To find the coefficient of linear expansion, we need to use the formula:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length
ΔT is the change in temperature
In this case, the change in length is given as 1.5 cm, the original length is 10.0 m, and the change in temperature is 90°F.
First, we need to convert the change in temperature from Fahrenheit to Celsius since the coefficient of linear expansion is typically given in terms of Celsius.
To convert Fahrenheit to Celsius, we use the formula:
°C = (°F - 32) * (5/9)
So, first, let's convert 90°F to Celsius:
°C = (90 - 32) * (5/9)
°C = 58 * (5/9)
°C ≈ 32.22
Now we have all the values needed to solve for the coefficient of linear expansion:
1.5 cm = α * 10.0 m * 32.22°C
Before proceeding, let's convert the change in length from cm to meters by dividing it by 100:
1.5 cm = 0.015 m
Now we can rearrange the equation to solve for α:
α = (0.015 m) / (10.0 m * 32.22°C)
α ≈ 4.65 x 10^-6 1/°C
Therefore, the coefficient of linear expansion is approximately 4.65 x 10^-6 1/°C.