Warr said:While reading a physics text, I came across an equation
[tex]l' = l + \alpha\,a[/tex], where [tex]\alpha[/tex] is the order of unity. What exactly does this phrase mean (ie if I knew l and a, what would [tex]\alpha[/tex] be?)
thanks
The equation "l' = l + $\alpha$a" is a mathematical expression used to represent the change in length of an object. The l' represents the final or changed length, l represents the initial length, $\alpha$ represents the coefficient of thermal expansion, and a represents the change in temperature.
The equation "l' = l + $\alpha$a" is commonly used in fields such as physics and engineering to understand the effects of temperature on the size and shape of objects. It can also be used in experiments to measure the coefficient of thermal expansion of various materials.
An example of how this equation is applied in real life is in the construction of bridges. Engineers use this equation to determine the amount of expansion joints needed in a bridge to allow for the expansion and contraction of the metal due to temperature changes.
The coefficient of thermal expansion (represented by $\alpha$) is a measure of how much a material expands or contracts when its temperature changes. It is an important factor in determining the change in length of an object due to temperature. Different materials have different coefficients of thermal expansion, which can affect the structural integrity of buildings and machines.
While the equation "l' = l + $\alpha$a" is a useful tool for understanding and predicting the effects of temperature on objects, it does have some limitations. It assumes that the coefficient of thermal expansion remains constant over a wide range of temperatures, which may not always be the case. Additionally, it does not take into account other factors such as stress or strain that may affect the length of an object.