What is the length of an aluminum rod at 65 C if its length at 15 C is 1.2 meters?
I will be happy to critique your thinking.
New length= oldlength(1+alpha*(65-15))
where alpha is the coefficent of linear expansion of aluminum
1.201386 meters
To find the length of the aluminum rod at 65°C, you can use the formula:
New length = old length * (1 + alpha * (T - T0))
In this formula:
- New length is the length of the rod at the desired temperature (65°C in this case).
- Old length is the length of the rod at a known temperature (15°C in this case).
- Alpha is the coefficient of linear expansion for aluminum.
- T is the desired temperature (65°C).
- T0 is the reference temperature (15°C in this case).
Given that the old length is 1.2 meters and the reference temperature is 15°C, we can substitute these values into the formula:
New length = 1.2 * (1 + alpha * (65 - 15))
Now you need to know the coefficient of linear expansion for aluminum, which is a material property. Let's assume the alpha value for aluminum is 0.000022 (1/°C), which is a typical value.
Substituting the alpha value into the formula, we get:
New length = 1.2 * (1 + 0.000022 * (65 - 15))
Now you can simplify the equation:
New length = 1.2 * (1 + 0.000022 * 50)
New length = 1.2 * (1 + 0.0011)
New length = 1.2 * 1.0011
New length = 1.201386 meters
So, the length of the aluminum rod at 65°C is approximately 1.201386 meters.