Science People: Help me with an uncertainty calculation

[Snoobper]

I need the uncertainty for log T:

log T=log(a+b(R/R0)-c(R/R0)^2)

where a, b, c are constants, and R has some uncertainty, δR, and R0 has some uncertainty, δR0.


Go, go, GO!

 

[-Bane]

Do your own lab homework.

 

[Snoobper]

Also, could I just use the relationship

T=a+b(R/R0)-c(R/R0)^2 to compute an uncertainty for some T value using the derivative method, and then just take the log of the uncertainty? Would that work?

 

[blazindave]

Tell them you are uncertain on how to get the answer.
Full marks guaranteed.

 

[Snoobper]

Do your own lab homework.

No sir!

 

[-Bane]

No sir!

k,

Uncertainty for any function f, delta-f, with variables x,y which both have some error delta-x and delta-y:

delta-f = |df/dx|delta-x + |df/dy|delta-y + ... (etc)

 

[-zYe-]

snoobper you turned out ok after all.

 

[-Bane]

You could find T, delta-T and then compute delta-log(T) as

delta-log(T) = |d(logT)/dT|*delta-T = (delta-T)/T

 

[Snoobper]

By using derivatives method, I can compute δT...

Can I just take the log of δT then say thats the uncertainty in log T?

 

[SirBatesAlot]

P=MV

 

[Snoobper]

snoobper you turned out ok after all.

I love you, you complete me.

 

[Lynx [TKB]]

By using derivatives method, I can compute δT...

Can I just take the log of δT then say thats the uncertainty in log T?

See what Bane said in the post above yours. Of course if the logarithm is base 10 then δ(logT) = δT / [ln(10) * T].

 

[Snoobper]

And so I have computed δT:
δT= |b(1/R0)-2c(R/R0)(1/R0)| δR + |-b(R/R0^2)-2c(R/R0)(-R/R0^2)| δR0
= |b(1/R0)-2c(R/R0^2)| δR + |-b(R/R0^2)+2c(R^2/R0^3)| δR0

You could find T, delta-T and then compute delta-log(T) as

delta-log(T) = |d(logT)/dT|*delta-T = (delta-T)/T

So,

δ log(T)= d(log(T))/dT * δT = δT/(ln (10)T)

Is this correct?

 

[Snoobper]

See what Bane said in the post above yours. Of course if the logarithm is base 10 then δ(logT) = δT / [ln(10) * T].

same result that I reached, thanks!

I suppose I'm good now, thanks TW denizens.

 

[Lynx [TKB]]

k,

Uncertainty for any function f, delta-f, with variables x,y which both have some error delta-x and delta-y:

delta-f = |df/dx|delta-x + |df/dy|delta-y + ... (etc)

Also, this will probably overestimate the error, giving you the maximum uncertainty. It might be a better idea to add the errors in quadrature:

i.e.

δf = sqrt[(|df/dx|*δx)^2 + ... + (|df/dn|*δn)^2]

 

[aNimAL]

hey snooby I got help wif my homework too except I'm a retarded imbecile who speaks redundantly

 

[Snoobper]

Also, this will probably overestimate the error, giving you the maximum uncertainty. It might be a better idea to add the errors in quadrature:

i.e.

δf = sqrt[(|df/dx|*δx)^2 + ... + (|df/dn|*δn)^2]

What's the idea behind this quadrature you speak of?

 

[Lynx [TKB]]

What's the idea behind this quadrature you speak of?

If you have an error that is calculated by δf = δx + δy you are assuming that x and y were underestimated or overestimated by their full amount. Since errors are generally random, there is also equal chance that x could have been underestimated while y was overestimated, i.e. δf = δx - δy. Adding in quadrature is just a way to average so you get more realistic uncertainties:
δf = sqrt[(δx)^2 + (δy)^2]

 

[Snoobper]

I see!

Thank you kind sir!