Which would take longer to cool off by 50 degrees, 1 kg of Copper or 1 kg of liquid water?
2 answers:
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Dimensional analysis is a method of checking the dimensions of each value in an equation. I will give you an example.
Is a know equation which equates energy and mass. So our question is, is this true or not? The method is following:
knowing that c has the dimension of [m/s] and m has [kg], what is the dimension of E? So here the dimensional analysis begins.
![E = mc^2 \Rightarrow [E] = \text{kg} \cdot \left( \frac{\text{m}} {\text{s}}\right)^2 = \text{kgms}^{-2}](https://tex.z-dn.net/?f=E%20%3D%20mc%5E2%20%5CRightarrow%20%5BE%5D%20%3D%20%5Ctext%7Bkg%7D%20%5Ccdot%20%5Cleft%28%20%5Cfrac%7B%5Ctext%7Bm%7D%7D%20%7B%5Ctext%7Bs%7D%7D%5Cright%29%5E2%20%3D%20%5Ctext%7Bkgms%7D%5E%7B-2%7D)
This can be used also to solve "equations" to prove certain dimensions of unknown constants.
Is a know equation which equates energy and mass. So our question is, is this true or not? The method is following:
knowing that c has the dimension of [m/s] and m has [kg], what is the dimension of E? So here the dimensional analysis begins.
This can be used also to solve "equations" to prove certain dimensions of unknown constants.