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Hello Physics Stack Exchange,

This is my first post on this forum, please correct me on any semantic mistakes I may make.

Recently in my physics class we did a lab on Heat Capacity, where we had a 250g iron weight (at room temperature) and a beaker with 300ml of water heated to approximately 100°C . The goal of the lab was to log the change in temperature of the water once the room temperature iron weight was placed into the beaker of water. We were to stop logging temperature when the drop became stagnant.

However, the beaker was insulated and we could not see inside it. As a result we didn't notice that the thermal probe was not in the water, therefore all our results were invalid.

My question to you: I'm writing a simulation to try and re-create valid data for our lab, assuming there are a lot of "perfect" values (such as the beaker was perfectly insulated) how would I calculate the change in temperature based on time?

I've seen this post on a similar subject however the equation presented in the solution does not make sense to me, and I'm not sure if I can apply it to my scenario.

EDIT: Simulating my data will not achieve me a better mark, as the data is only required for calculations. The data needs to match the lab's criteria, but the data accuracy will not influence my grade.

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    $\begingroup$ Do the lab again, and get good data. $\endgroup$ – David White May 3 '16 at 1:03
  • $\begingroup$ Not an option. We only had one chance to do the lab. I'm looking for a mathematical solution at this point. $\endgroup$ – Netwinder May 3 '16 at 1:05
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    $\begingroup$ I reread that comment a few times, and I understand your point. Real world observations would be nice, however if I included the simulated data I would mark it as a "simulation" not "reality" $\endgroup$ – Netwinder May 3 '16 at 1:14
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    $\begingroup$ Talk to your teacher, explain what happened, and ask him or her what acceptable options would be. Don't guess what he or she might accept. Borrowing someone else's data might be perfectly ok, but a simulation not. Or vice versa. You won't know unless you ask! $\endgroup$ – garyp May 3 '16 at 2:16
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    $\begingroup$ I've talked to the teacher and he told me that my data is only used for calculations, therefore simulating it is perfectly fine. Does somebody here know thermodynamics, and can give me a solution? $\endgroup$ – Netwinder May 3 '16 at 2:22
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You will require the specific heat capacity values of water, beaker and iron assuming what you used in the lab was pure iron weight. these are usually available online. now principle of calorimetry tells us that assuming no heat is lost to the surroundings heat lost by the hot body is equal to heat gained by the cold body. let room temperature be T(r) and final temperature reached be T(f).

Now heat lost by water= mass of water * S(w) * (100-T(f)). heat lost by beaker=mass of beaker * S(b) * (100-T(f)).

here T(f) is expressed in celsius and S(w) is specific heat capacity of water, etc. Equate this to heat gained by the iron

heat gained= mass of iron * S(Fe) * (T(f)-T(r))

Solve for T(f).

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