Calorimetry Lab Analysis (predict specific heat of unknown metal)

[Wubblyboofus]

Homework Statement

so we did an experiment. basically the teacher gave us each a cube of unknown metal
and we had to figure out what it was using the specific heat.

we put the metal in boiling water until it was 212C
and then we put it in room temp water
and we measured how much it heated the water

he also gave us some lead to find the specific heat of so we can troubleshoot if our data is wrong because of the lab process or the calculation

check out the attached files for more precise instructions

so my results are in this google sheets
i set it so anyone with link can view so you guys should have no problem viewing it
https://docs.google.com/spreadsheets/d/1StBNPECq3Ny0tK_N6-0DT4JGgR_bm3tCwsx2dP8RO_0/edit?usp=sharing

i tried making formulas on some of the data so that i didnt have to do the calculations by hand but something is wrong. im getting 50 J/gC (joules per grams degrees celcius) for my unknown metal, which has to be wrong because the specific heat of water is 4.184 J/gC and water is known to have a high specific heat

please help me
im not sure if this is because of my procedure or my calculations
thank you

Relevant Equations

final temperature minus initial temperature = change in temperature
specific heat times mass times change in temp. = change in heat

Problem Statement: so we did an experiment. basically the teacher gave us each a cube of unknown metal
and we had to figure out what it was using the specific heat.

we put the metal in boiling water until it was 212C
and then we put it in room temp water
and we measured how much it heated the water

he also gave us some lead to find the specific heat of so we can troubleshoot if our data is wrong because of the lab process or the calculation

check out the attached files for more precise instructions

so my results are in this google sheets
i set it so anyone with link can view so you guys should have no problem viewing it
https://docs.google.com/spreadsheets/d/1StBNPECq3Ny0tK_N6-0DT4JGgR_bm3tCwsx2dP8RO_0/edit?usp=sharing

i tried making formulas on some of the data so that i didnt have to do the calculations by hand but something is wrong. I am getting 50 J/gC (joules per grams degrees celcius) for my unknown metal, which has to be wrong because the specific heat of water is 4.184 J/gC and water is known to have a high specific heat

please help me
im not sure if this is because of my procedure or my calculations
thank you
Relevant Equations: final temperature minus initial temperature = change in temperature
specific heat times mass times change in temp. = change in heat


the above is my data from my lab

ive tried to do calculations on paper but i get the same results as in the above spreadsheet
but i know that specific heat is way off...

 

[Wubblyboofus]

i don't know what you guys consider to be introductory or advanced physics but i put it in advanced cus i thought it was pretty hard lol

 

[Wubblyboofus]

below is an edited file of the one in the original post. i already did what is on this doc on paper. i just rewrote it on this doc so you guys can see my work

 

[tech99]

"tf water" may be a mistake, as for calculation purposes this is the initial temp of the metal. The final temp of the water is about 26C and not around boiling. I also notice you have confused Centigrade and Fahrenheit for the boiling water.

 

[Chestermiller]

Let's see the equations you used. If you don't show us those, how are we supposed to help you?

 

[Wubblyboofus]

"tf water" may be a mistake, as for calculation purposes this is the initial temp of the metal. The final temp of the water is about 26C and not around boiling. I also notice you have confused Centigrade and Fahrenheit for the boiling water.

the water ti and tf is how much the room temperature water was heated once the metal (at 212 C) was placed into it. so it goes from about 21 to 26 because the water has high specific heat so it is hard to raise its temperature even if a block of boiling metal is placed into it.
the metal ti and tf however is how much the metal was heated once placed into boiling water. so that would be from 21 to 212.

as i said earlier the procedure went as follows:
put metal into boiling water
metal is now at boiling temperature
put that same metal into room temp water
see how much the room temp water heats
calculate specific heat of metal
use that to identify the metal

 

[Wubblyboofus]

Let's see the equations you used. If you don't show us those, how are we supposed to help you?

final temperature minus initial temperature = change in temperature
specific heat times mass times change in temp. = change in heat
SH * m * delta T = delta H

i don't think we need the ideal law of gases even though we learned it along with these formulas in class but i might be wrong

 

[Chestermiller]

I still can't tell from the "equation" you wrote what you did. Here is my understanding of the equation to use: $$m_{cube}C_{cube}(T_{0, cube}-T_{final})=m_{water}C_{water}(T_{final}-T_{0,water})$$where the subscript 0 refers to the initial temperatures of the cube and the water, and the subscript final refers to the final equilibrated temperature of both the cube and water. Is this what you were trying to write? If so, you need to be more precise in writing your equations. If not, where do we differ and why?

 

[Wubblyboofus]

I still can't tell from the "equation" you wrote what you did. Here is my understanding of the equation to use: $$m_{cube}C_{cube}(T_{0, cube}-T_{final})=m_{water}C_{water}(T_{final}-T_{0,water})$$where the subscript 0 refers to the initial temperatures of the cube and the water, and the subscript final refers to the final equilibrated temperature of both the cube and water. Is this what you were trying to write? If so, you need to be more precise in writing your equations. If not, where do we differ and why?

yes! that is exactly what i wanted
thats what we learned in class

how did you write that in here lol

 

[Wubblyboofus]

mass of water * change in temp of water * specific heat of water = change in heat of water AND cube = mass of cube * change in temp of cube * specific heat of cube

because we know that the change in heat is equal between the water and the cube we can set it equal

because even though the change in temp is different, the change in heat is equal

 

[Chestermiller]

yes! that is exactly what i wanted
thats what we learned in class

how did you write that in here lol

https://www.physicsforums.com/help/latexhelp/ lol

So from this equation, what result (algebraic equation) do you get if you solve the equation I wrote for $C_{cube}$?

 

[Wubblyboofus]

specific heat of cube = mass of water * change in temp of water * specific heat of water / change in temp of cube / mass of cube

in which / means divide and * means multiply

 

[Wubblyboofus]

SP cube = 30 * 187.5 * 4.184 / 3.8 / 121.5
SP cube = 50.97

but it should not be 50.97
because the specific heat of water is 4.184
and water is known to have a high specific heat
and metals almost always have specific heats of less than 1

so something is wrong here

 

[Gaussian97]

Are you taking into account that the calorimeter will have loses?

 

[Wubblyboofus]

Are you taking into account that the calorimeter will have loses?

we are not using a calorimeter
we are using thermometers

there will be inaccuracies in our data because the time it takes to put the boiling metal from the boiling water to the room temp water will affect the accuracy a bit

 

[ZapperZ]

You are still not acknowledging that you are confusing temperature in F and C. You kept writing that the boiling temperature is 212 C. This is incorrect. It is at 212 F or 100 C. And in using the specific heat equation, the change in temperature must be in C (or K), not F.

Zz.

 

[Wubblyboofus]

You are still not acknowledging that you are confusing temperature in F and C. You kept writing that the boiling temperature is 212 C. This is incorrect. It is at 212 F or 100 C. And in using the specific heat equation, the change in temperature must be in C (or K), not F.

ohhhhhhhh
im sorry. thank you for explaining it more clearly. i will go change it

also i don't think change in C or change in K matters
because K is just C + 273.15
so the change would be the same
and in class we learned it with C

 

[ZapperZ]

ohhhhhhhh
im sorry. thank you for explaining it more clearly. i will go change it

also i don't think change in C or change in K matters
because K is just C + 273.15
so the change would be the same
and in class we learned it with C

Isn't that what I wrote? I said ".. in using the specific heat equation, the change in temperature must be in C (or K), not F... ".

I included "K" to be complete in case you are going on further and start to deal with the ideal gas law. In such a case, the absolute temperature is required, not just the change in temperature.

Zz.

 

[Wubblyboofus]

Isn't that what I wrote? I said ".. in using the specific heat equation, the change in temperature must be in C (or K), not F... ".

I included "K" to be complete in case you are going on further and start to deal with the ideal gas law. In such a case, the absolute temperature is required, not just the change in temperature.

Zz.

do you think i need ideal gas law?
and do you think you can help me with the thing on google sheets?

 

[Wubblyboofus]

also i can't seem to edit the original post

 

[Chestermiller]

How can the final temperature of the water be different from the final temperature of cube at equilibrium? And, how did you measure the final temperature of the cube?

 

[Wubblyboofus]

How can the final temperature of the water be different from the final temperature of cube at equilibrium? And, how did you measure the final temperature of the cube?

the initial temp of the cube if before i put it into the boiling water
the final temp of the cube is after i put it in the boiling water for a couple minutes
the initial temp of the water is room temp (before i put the boiling cube in)
the final temp of the water is the highest temp the room temp water becomes after putting the cube in

 

[Chestermiller]

do you think i need ideal gas law?

What could possibly make you think this?

and do you think you can help me with the thing on google sheets?

There is something very wrong with the data presented in your data sheets.

 

[Wubblyboofus]

And, how did you measure the final temperature of the cube?

i did not need to measure the final temp of the cube because boiling water is always 100C
so the cube must be 100C after a couple minutes

 

[Wubblyboofus]

What could possibly make you think this?

well the formula I've been using doesn't seem to give me the right answer
it gives me 20 something J/gC
when i should be getting less than 1 J/gC

 

[Chestermiller]

well the formula I've been using doesn't seem to give me the right answer
it gives me 20 something J/gC
when i should be getting less than 1 J/gC

So any other wild ass choice of an equation is fair game?

The reason you are getting the wrong answer is not because of the equation you are implementing. It is because of the wrong way that you are implementing the equation. In each of the cases, please list the initial and final temperatures (all in degrees C) of the cube and of the water. Thanks.

 

[Wubblyboofus]

So any other wild ass choice of an equation is fair game?

The reason you are getting the wrong answer is not because of the equation you are implementing. It is because of the wrong way that you are implementing the equation. In each of the cases, please list the initial and final temperatures (all in degrees C) of the cube and of the water. Thanks.

umm i did

dont look at the bottom three trials
those are for lead
the teacher told us that was lead so we could test our procedure on that as practice

the first three trials are the ones about the unknown metal cube he gave us
i filled in all the information you need

 

[Chestermiller]

the initial temp of the cube if before i put it into the boiling water
the final temp of the cube is after i put it in the boiling water for a couple minutes
the initial temp of the water is room temp (before i put the boiling cube in)
the final temp of the water is the highest temp the room temp water becomes after putting the cube in

According to your data sheet (as I understand it), the water temperature rose to about 100 C, and the cube temperature dropped to about 26 C. Is this a correct interpretation? Or was the final temperature of both the water and the cube 26 C?

 

[Wubblyboofus]

gosh dang it
i am so dumb
the initial temp for the cube is 100C not 21C
lkajsdfoanoginlkadjfkalkdlknkladjglkalkdjflkajlkdjlkgjaklsdjglajlgd
i wasted so much time of my life repeatedly putting this wrong information into my calculator

 

[Wubblyboofus]

now my specific heat is negative 1
great
lol

 

[ZapperZ]

do you think i need ideal gas law?

I have no idea, because I don't know what you are doing. Besides, this is not relevant to your question in this thread.

and do you think you can help me with the thing on google sheets?

A what?

Zz.

 

[Chestermiller]

$$C_{cube}=\frac{(30)(4.184)(26-20)}{(121.5)(100-26)}$$

?

 

[Wubblyboofus]

I have no idea, because I don't know what you are doing. Besides, this is not relevant to your question in this thread.

well it turns out i don't need it as someone else explained to me

and google sheets is the thing that is kinda like microsoft excel that let's you make spreadsheets

 

[Wubblyboofus]

$$C_{cube}=\frac{(30)(4.184)(26-20)}{(121.5)(100-26)}$$

?

0.084

 

[Wubblyboofus]

now we just need to find it for the other two trials, average it, and then find the metal with that specific heat

thank you so much!