How Do You Calculate the Error on Variables in an Equation?

[Exulus]

Hi guys..i always seem to forget how to calculate errors and end up confusing myself in a giant mess...so any help much appreciated.

I have 24.98 +/- 1.05 = e/(nkT)

And i need to work out n, i know all the other numbers (which are constants and have no errors). So firstly how do i calculate the error on n if all of the others are constant, and secondly how would i calculate the error on n if T also had an error? Cheers :)

 

[dextercioby]

1.St question:do u know calculus??Your function mai be written (via logaritmation)
$$nkT=\ln(24.98\pm1.05)$$

Express "n" and "$\Delta n$" in terms "T" and "$\Delta T$" respectively.

Daniel.

 

[Exulus]

oops, sorry, i didnt explain the equation clearly enough. "e" in this case doesn't stand for exponential, its the charge of an electron (k is the Boltzmann constant and T is temperature).

 

[dextercioby]

AAAA...That changes thing a little bit,not too much.You didn't answer to my question,though...Do u know calculus??
Then the function would be:
$$n=\frac{e}{(24.98 \pm 1.05) k} \frac{1}{T}$$

Can u differentiate a function??

Daniel.

 

[Exulus]

Hi,

Yeah i can differentiate..but what bit would i need to differentiate and why?

 

[Exulus]

Has this thread been forgotton about? :( Sorry i just don't even know where to start with errors when it gets more complicated than adding/subtracting...

Do you want me to differentiate every letter? Would that require using the product rule twice? Am i going in completely the wrong direction with this? Why do you need to differentiate to find errors? Thanks for any help so far :)

 

[dextercioby]

Because that's the theory of errors...Involves partial (in this case one variable,namely T) differentiation.

$$\Delta n=|\frac{dn(T)}{dT}|\Delta T$$

,where $\Delta T$ is the error in temperature,and the corresponding $\Delta n$ is the error in concentration...

Daniel.

 

[Exulus]

So if I've understood you correctly:

$$\Delta n={-T}^{-2}\Delta T$$

? :)

 

[dextercioby]

U didn't.

1.What happened to the constants?
2.The minus does not exist.It's "erased" by the modulus/absolute value.There's never minus in error theory...All errors must add...

Daniel.

 

[Exulus]

Whoops! Lemme try again...

$$\Delta n=\frac{e}{(24.98 \pm 1.05) k}\ {T}^{-2}\Delta T$$

Is that right? Cheers for the patience

 

[dextercioby]

It looks okay,though that $\pm$ in the denominator looks kinda weird...

Daniel.