Specific heat capacity coursework

[kieyard]

Homework Statement

earlier today i was doing some coursework to find the specific heat capacity of an unknown metal by submersing 100g / 0.1kg of the metal in boiling water above 75°C and record the temperature after 30 seconds (θ_m).
we then had to transfer the the metal from the boiling water into 70ml of cool/ room temp water which we had recorded the temperature before hand (θ₁) and the maximum temperature reached after adding the metal (θ₂).
we had then got to calculate the energy the water had gained from the metal block using E=mc(θ₂-θ₁)
we then had to repeat the experiment again but this time using a lower starting temp of somewhere between 60°C-70°C and record our reading and calculate energy gained again.
the following task was then to calculate the specific heat capacity of the metal by equating the energy gained by the water to the energy lost by the metal using E=mc(θ_m-θ₂) for both sets of recorings
we then had to comment on why the two values of c (specific heat capacity) were different.

Homework Equations

E=mcΔT

The Attempt at a Solution

i can not remember exact values but as expected in the experiment i observed a higher amount of energy gained by the water in the experiment where the metal started above 75°C

however for the second experiment i got a higher specific heat capacity which apparently i shouldn't of got because thermal energy is lost faster to the surroundings during the transfer the hotter the starting temperature is.
but surely a if energy is lost not heating the water then the metal wouldn't heat the water up as much as it should of and as c is proportional to E/ΔT. as ΔT of the metal is greater than it should be because it lost the energy instead of heating up the water. my working says i am right.

to try and clear that last paragraph up a bit better. here's some results like mine.

as shown on the pic as A increases, C increases. and A should be higher than what it is because the metal lost a lot of energy due to its high starting temp and therefore didnt heat up the water as much as it should of. thus we can assume that the metals metaling point is higher than 588°C

in the second experiment we start at a lower temp and this means less energy is lost as less energy is lost during the transfer of the metal from beaker to beaker so we can assume that this trial is more accurate and from the previous reasoning actual C is higher than 588°C and as trail Y is more accurate you should presume C in Y to be higher than C in X.

i explained this to my teacher but she still says its wrong but couldn't explain why, any help would be appreciated why/why not i am right/wrong.

 

[CWatters]

Perhaps not the whole problem but.. check 69-32=?

PS: Your temperatures are recorded to whole degrees. As an experiment see what an error of 1C makes to the answer. For example if the second experiment produced a rise of 7 rather than 8C what would the specific heat capacity work out as?

 

[kieyard]

oops what a silly mistake but as you can still see its higher than the first test. but if i do use 7°C it becomes lower but that doesn't answer why my reasoning is wrong. what am i doing wrong in my reasoning? surely as the second is more efficient as less thermal energy is lost due to the exponential properties of heat it would give a more accurate value of C and if the first one was more efficient it would give a higher reading therefore you can presume the second one should give a higher value of C .

 

[CWatters]

You are correct in that at lower temperatures the losses should be less and that should make Cm more accurate however lower temperatures can cause another problem ...

At lower temperatures the temperature changes (Θ₂ - Θ₁ and Θ_m - Θ₂) are smaller. You can only measure the temperature with a certain accuracy (say +/1 degree) so the percentage error increases as the temperature changes get smaller. One of the golden rules when trying to improve accuracy is to try and avoid (design out) the need to "subtract similar numbers" because of the extreme effect that can have on error propagation.