Main Question or Discussion Point
I have a question that sounds easy but as of yet noone has been able to give me a satisfactory explaination. I made a plot of mobility (cm^2/Vs) against temperature (K), i then wanted to find an expression that showed the relationship between the two. What i did was took the natural logarithm of both mobility and temperature and plotted that. This gave me a straight line (R^2 = 0.9997). So i then rearranged this straight line equation to see how mobility related to temperature. I have attached a file with the plots, data and my working out. I came up with the equation: mobility = Const/(Temp^0.63). This equation does give me the values of mobility (in cm^2/Vs) when i put in temperatures (in Kelvin) that i was looking for. However, when i was thinking about the dimensions of the equation it did not seem to make physical sense. When you log or take the exponent of something, the something has to be dimensionless. I have asked some people about this, someone said that most of the time this sort of thing is just ignored and someone else told me to take the log of a ratio, to have T/T0 where T0 is some sort of reference temperature. However in my system there is no physics reason to have a reference temperature and i am happy with the equation that i have come up with as it gives me the values i was looking for. Its just the dimensions that i dont understand. If you log something with units, then take the exponent of it, does the thing you get back with have the same units as when you started? how do you go about logging things with units?
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