Why the folloowing expression T/K=t degree celcius+273.15 is dimensionally correct?

Question

It is a question of Vector chapter in Physics in the level of class XI & XII

Answer 1

Temp is measured in kelvins, so T / K is dimensionless.

273.15 is dimensionless.

t (degree celcius) means take the temp in degrees celcius and strip the units, so that is dimensionless.

For consistency, I probably would have written it
T (K) = T (C) + 273.15

Anyway, it all adds up I suppose.

Answer 2

I'm really glad the first two answers knew what you were asking...I certainly did not. Since you failed to specify what T, K, and t are, I have no idea what their dimensions should be. I can guess, because of the 273 which is the offset in degrees between Kelvin and Centigrade. But, in physics and the other hard sciences, guessing is not a good thing.

And I'm with Bekki why would you not use K = T + 273 to convert Centigrade (T) to Kelvin (K)? I can solve K = T + 273 so that 1 = (T + 273)/K = T/K + 273/K and T/K = 273/K - 1 But as you can plainly see, this is nowhere close to the same thing you are showing.

And, to a point, T/K is in fact dimensionless; so your dimensions are correct, but I've no clue what t is. I mean, if T/K = t/273, what's T273/K = t = ? = degree^2/degree = degree.

Answer 3

The two units of measurement have equal degree measures, that is to say, that an interval of 1 degree celcius is the same as that of 1 kelvin. The difference is that they do not have the same referrence, or 'zero' point. So they are dimensionally the same. Remeber that simple addition, as shown in the equation, that not affect dimensions.

Answer 4

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The expression T/K= t degree Celsius +273.15 is dimensionally correct because temperature is dimensionless.

The left hand side is dimensionless and right hand side consists of two dimensionless terms ( t degree Celsius and 273.15 )
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