Thermal physics phase change: Liquid copper to solid

[DracoMalfoy]

Homework Statement

How much energy must be removed from the system to turn liquid copper of mass 1.5kg at 1083 degrees celsius to solid copper at 1000 degrees celsius?

a. -2.49X10^5J

b. -3.67X10^4J

c. 2.25X10^3J

d. 9.45X10^4J

e. -2.78X10^3J

Homework Equations

Q=Mc(Tf-Ti)
Qtot=Q1+QLf+Q2[/B]

The Attempt at a Solution

Qliqcop+MLf+Qcopsolid=Qtot

M1C1(Tf-Ti)+ MLF+ M2C2(Tf-Ti)=Qtot

(1.5)(.49)(0-1083)+(1.5)(387)+(1.5)(1000-0)=Qtot

Im pretty sure I am doing this incorrectly...

 

[ZapperZ]

The Attempt at a Solution

Qliqcop+MLf+Qcopsolid=Qtot

M1C1(Tf-Ti)+ MLF+ M2C2(Tf-Ti)=Qtot

(1.5)(.49)(0-1083)+(1.5)(387)+(1.5)(1000-0)=Qtot

Im pretty sure I am doing this incorrectly...

There is something weird going on here. You keep having a "0 C" in your Tf or Ti. Where is there a zero degree temperature in the problem?

There are only two processes from what I can tell. The Cu is already at its melting temperature. So there is a latent heat of fusion process as it turns from liquid into solid. That's one process. The second is when after it has turned into solid, it cools down to 1000 C. That's it! I do not understand why you have three terms in your heat equation.

Please note that ΔT = T_f - T_i is the change in temperature of the object. Nothing here is changing from 0 C, or changing to 0 C. So I am puzzled by the inclusion of this temperature in your equation. This appears to be your biggest mistake.

Zz.

 

[DracoMalfoy]

There is something weird going on here. You keep having a "0 C" in your Tf or Ti. Where is there a zero degree temperature in the problem?

There are only two processes from what I can tell. The Cu is already at its melting temperature. So there is a latent heat of fusion process as it turns from liquid into solid. That's one process. The second is when after it has turned into solid, it cools down to 1000 C. That's it! I do not understand why you have three terms in your heat equation.

Please note that ΔT = T_f - T_i is the change in temperature of the object. Nothing here is changing from 0 C, or changing to 0 C. So I am puzzled by the inclusion of this temperature in your equation. This appears to be your biggest mistake.

Zz.

I figured that. I am getting a bit frustrated. i knew that i was doing it wrong. i keep getting an answer around 5.8x10^5. This is really difficult for me, and i don't have a very good teacher.

 

[DracoMalfoy]

I figured that. I am getting a bit frustrated. i knew that i was doing it wrong. i keep getting an answer around 5.8x10^5. This is really difficult for me, and i don't have a very good teacher.

i really don't know what I am doing here...

 

[ZapperZ]

I figured that. I am getting a bit frustrated. i knew that i was doing it wrong. i keep getting an answer around 5.8x10^5. This is really difficult for me, and i don't have a very good teacher.

i really don't know what I am doing here...

You did not indicate if anything I had said above help you in solving the problem. If it did not, what exact that you don't understand here?

Zz.

 

[DracoMalfoy]

You did not indicate if anything I had said above help you in solving the problem. If it did not, what exact that you don't understand here?

Zz.

The temperatures. I was following an example that we did in class. I am not understanding. I guet that nothing is changing from 0 to whatever temperature in the problem. I think i see that now. Its just how I am supposed to set up the equation.

 

[ZapperZ]

The temperatures. I was following an example that we did in class. I am not understanding. I guet that nothing is changing from 0 to whatever temperature in the problem. I think i see that now. Its just how I am supposed to set up the equation.

You obviously are familiar with these two equations, since you used it in your first post:

1. Q = mc ΔT
2. Q = mL_f

Do the process one at a time. When the liquid copper, at its melting point, is changing from liquid to solid, what is the total heat given off when all of it changed from liquid to solid?

Zz.

 

[DracoMalfoy]

You obviously are familiar with these two equations, since you used it in your first post:

1. Q = mc ΔT
2. Q = mL_f

Do the process one at a time. When the liquid copper, at its melting point, is changing from liquid to solid, what is the total heat given off when all of it changed from liquid to solid?

Zz.

mc ΔT+mL

You obviously are familiar with these two equations, since you used it in your first post:

1. Q = mc ΔT
2. Q = mL_f

Do the process one at a time. When the liquid copper, at its melting point, is changing from liquid to solid, what is the total heat given off when all of it changed from liquid to solid?

Zz.

so mc ΔT+mL+mc ΔT=Qtot? I am sorry if it seems like I am a complete idiot with this. I am really trying to figure this out. Its really difficult for me. I am not understanding and I am getting really frustrated...

 

[DracoMalfoy]

mc ΔT+mLso mc ΔT+mL+mc ΔT=Qtot? I am sorry if it seems like I am a complete idiot with this. I am really trying to figure this out. Its really difficult for me. I am not understanding and I am getting really frustrated...

Qtot= Mc(Tf-Ti)+ MLf

= (1.5)(387)(1000-1083)+ (1.5)(134x10^4)
im not getting the answer with anything that i try doing

 

[gneill]

What is the source for your numbers 387 and 134x10^4? What units are associated with those numbers?

 

[DracoMalfoy]

387 j/kg degreeC is specific heat (https://cnx.org/contents/Ax2o07Ul@10.1:XA0Vd8Dc@6/Temperature-Change-and-Heat-Capacity) and 134 comes from here as Lf (https://cnx.org/contents/Ax2o07Ul@10.1:Xyta70lI@9/Phase-Change-and-Latent-Heat)

 

[gneill]

Okay, so the first thing to note is kJ means thousands of joules, so 10³ is the multiplier for your latent heat of fusion. Second, the number on that web page is dubious because other sources place the latent heat of fusion for copper at about 208 kJ/kg. Other sources also place the specific heat of solid copper at 385 J/(kg °C).

Are you required to use those specific numbers or was this just a resource you picked? (it sometimes helps to check against other published numbers). Your course textbook may provide these values in a table in the back of the book.

 

[DracoMalfoy]

Okay, so the first thing to note is kJ means thousands of joules, so 10³ is the multiplier for your latent heat of fusion. Second, the number on that web page is dubious because other sources place the latent heat of fusion for copper at about 208 kJ/kg. Other sources also place the specific heat of solid copper at 385 J/(kg °C).

Are you required to use those specific numbers or was this just a resource you picked? (it sometimes helps to check against other published numbers). Your course textbook may provide these values in a table in the back of the book.

these sources are given to us by our teacher but I guess it depends on where you go to find them. I've been told that none of the answers are the correct choice but that's impossible ._. I haven't looked in the textbook yet. I am still confused on whether or the answer is supposed to be positive or negative. if the copper is cooling and energy is removed, that makes it negative right?

 

[gneill]

these sources are given to us by our teacher but I guess it depends on where you go to find them.

Okay, not sure what that means. A particular web page URL should have only one destination. If you are given specific instruction to use a specific source for your numbers, then those are the numbers to use.

Ive been told that none of the answers are the correct choice but that's impossible .

No, not impossible. Here at PF we've seen many instances where the "book answer" has been incorrect. Often it's due to a change being made to the question and the answer not being re-calculated.

im still confused on whether or the answer is supposed to be positive or negative. if the copper is cooling and energy is removed, that makes it negative right?

They're asking for how much energy must be removed. That sounds like a number-count/quantity kind of thing, so an absolute value (positive number) would be implied.

 

[ZapperZ]

mc ΔT+mLso mc ΔT+mL+mc ΔT=Qtot? I am sorry if it seems like I am a complete idiot with this. I am really trying to figure this out. Its really difficult for me. I am not understanding and I am getting really frustrated...

I asked you to do one process at a time! I asked first for the heat given off by liquid copper when it solidifies. You have not given me that.

If you can't do this simplest part, then we have a more fundamental issue to deal with.

Zz.

 

[CWatters]

First step is to understand what's happening in the question. They tell you you are starting with liquid copper at its melting point. So to turn it into a solid at a lower temperature you have to do two things...

1) Remove the latent heat of fusion/melting. This is the energy needed for the phase change only. It occurs at constant temperature so there is no delta T term in the equation.

2) Then you have to remove energy to cool down the now solid copper. The constant you need for this is the Specific Heat Capacity of solid copper (this could be different to the Specific Heat Capacity of liquid copper so check you have the right one).

Zapper suggested you just calculate the energy in step 1) first and post your working.