# 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 65Â°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 (65Â°C in this case).
- Old length is the length of the rod at a known temperature (15Â°C in this case).
- Alpha is the coefficient of linear expansion for aluminum.
- T is the desired temperature (65Â°C).
- T0 is the reference temperature (15Â°C in this case).

Given that the old length is 1.2 meters and the reference temperature is 15Â°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/Â°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 65Â°C is approximately 1.201386 meters.