A bar made of a particular metallic alloy has a length of 10 cm at a temperature of 24 oC and a length of 10.015 cm at the boiling point of water.
(a) If a second bar made of the same material were 10 m at 24 oC, how much longer would this bar be at the boiling point of water?
The answer has to be in cm. So i converted 10m to cm, 1000 and then put on the .015. Ended up with 1000.015. and that's wrong. I need to find delta L. I know this is dealing with thermal expansion, but I need help figuring out how to do this.
the answer is 1.5cm
To solve this problem, we need to use the concept of thermal expansion of solids. The linear expansion of a solid is given by the equation:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion of the material, L is the original length, and ΔT is the change in temperature.
Given:
Original length (L1) = 10 cm
Final length (L2) = 10.015 cm
Temperature change (ΔT) = boiling point of water - 24 oC
First, we need to find the coefficient of linear expansion (α) for the given material. This value may be provided in the problem statement or can be researched based on the material.
Once we have the coefficient of linear expansion (α), we can use the formula to find the change in length (ΔL) for the first bar.
ΔL1 = α * L1 * ΔT
Now, let's move on to the second part of the problem.
Given:
Original length (L1) = 10 m (which is equivalent to 1000 cm)
Final length (L2) = ?
Temperature change (ΔT) = boiling point of water - 24 oC
We need to find the change in length (ΔL2) for the second bar. Here, we can use the same coefficient of linear expansion (α) as the material is the same.
ΔL2 = α * L2 * ΔT
We want to find the final length of the second bar, which can be calculated as:
L2 = L1 + ΔL2
Substituting the value of ΔL2:
L2 = L1 + (α * L2 * ΔT)
Solving this equation will give us the final length (L2) of the bar at the boiling point of water.
It's important to note that the value you obtained, 1000.015 cm, is incorrect as you need to consider the change in temperature and the coefficient of linear expansion while finding the change in length (ΔL2).