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.
L = Lo + k*Lo(T - To).
Lo = Initial length.
To = Initial temperature.
L = 10 + k*10(100 - 24) = 10.015,
10 + 760k = 10.015,
760k = 10.015 - 10 = 0.015,
k = 1.974*10^-5 = Coefficient of linear expansion.
a. L=1000 + 1.974*10^-5*1000(100 - 24),
L = 1000 + 1.974*10^-5*76000,
L = 1000 + 1.50024 = 1001.500cm.
When you converted to cm, you multiplied by 100. Therefore you'll
have to multiply the 0.015 by 100 also.
Then you'll get 1000 + 1.5 = 1001.5cm,
To find out how much longer the second bar would be at the boiling point of water, we need to calculate the change in length (ΔL) using the concept of thermal expansion.
The formula for linear expansion is given as:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L0 is the original length, and
ΔT is the change in temperature.
We know that the change in temperature is from 24 oC to the boiling point of water (100 oC).
The coefficient of linear expansion (α) is a material-dependent constant. Since it is not provided in the question, you may need to refer to a table of material properties or search for the coefficient of linear expansion for the specific metallic alloy mentioned.
Once you have the coefficient of linear expansion (α), you can use it to calculate the change in length (ΔL) for the second bar.
Let's assume the coefficient of linear expansion (α) is 0.000012 (a typical value for metals).
For a bar initially measuring 10 cm at 24 oC:
ΔL = 0.000012 * 10 cm * (100 oC - 24 oC)
ΔL = 0.000012 * 10 cm * 76 oC
ΔL ≈ 0.00912 cm
So, the second bar would be approximately 0.00912 cm longer at the boiling point of water compared to its initial length at 24 oC.
Note: Your approach of converting 10 m to cm (1000 cm) and adding 0.015 cm is incorrect because thermal expansion calculations involve the change in length due to temperature, not the total length.