Heyo,
I'm being asked to show how I would calculate error for a specific heat capacity depth study using a calorimeter, in short the depth study is simply measuring the transfer of heat from a metal to water and working backwards to find the specific heat of the metal.
The formula is: Q = mcΔt
Q = energy transferred (J)
m = mass of the water (in kg) +/- 0.005 (measured using scales)
Δt = change in temperature of the water (in C) +/- 0.05 (measured using a calorimeter)
c = specific heat capacity for water (in J/kg/C) which is 4.1813 (im not sure what error I would include here as its an pre-determined value off the internet)
So now I think I can do this, again please let me know if this is wrong because I'm a year 11 student who has no idea what he's doing:
Add all the percentage errors So I think, from what the internet has told me, I would simply calculate the percentage error of each variable (m, Δt and c) and simply add them up.
Worked example:
Δt is calculated using the following formula (T_final - T_initial = Δt), so im not sure if I have to add the percentage error of both readings or if I can leave it as ±0.05 either way I said:
Δt = 2.1±0.05 which is a ±2.5% error
m = 8.12±0.005 which is a ±0.0625% error
c = 4.1813±0.00005 which is 0.0011958% error
From here I plugged my values without their error into the formula:
Q = mcΔt
Q = 8.12 × 4.18 × 2.1
Q = 71.22736 J
I then added the error of all my components below:
0.0625 + 2.5 + 0.0011958 = 2.5636968
So my answer would be 71.22736±2.5636968%
But that just looks disgusting so I have like no idea at all
She mentioned something about propagation of error and linked me to this pdf:
https://www.animations.physics.unsw.edu.au/sf/toolkits/Errors_and_Error_Estimation.pdfBut like im gonna be honest I have no idea what I'm doing at all, the internet isn't being very helpful and I keep running into dead ends and my head hurts as well which sucks but yea
Please, I will be forever grateful if you assist me in my conquest.
Thanks, Casey