How Do You Calculate Entropy Change in Thermodynamics Problems?

Click For Summary

Homework Help Overview

The discussion revolves around calculating the change in entropy in a thermodynamics context, specifically involving the cooling of gold and its interaction with surrounding materials. Participants are exploring the application of the entropy formula ΔS=Q/T and the implications of heat transfer in this scenario.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to determine the heat flow into the surroundings and how to calculate the change in entropy for both the gold and the surroundings. There are questions about the relevance of time in the context of heat transfer and whether the temperature of the surroundings changes during the process.

Discussion Status

Some participants have provided calculations for heat transfer and entropy change, while others have raised questions about the assumptions made regarding the specific heat of gold and the effects of gravitational potential energy. Guidance has been offered regarding the calculation of latent heat and its impact on the overall entropy change.

Contextual Notes

Participants note the absence of specific heat values in their reference materials and discuss the implications of using different states of matter (liquid vs. solid) for gold in their calculations. There is an acknowledgment of the need to consider the latent heat of fusion in the overall analysis.

physninj
Messages
37
Reaction score
0

Homework Statement


http://postimage.org/image/9artvc1h5/ see attached


Homework Equations


ΔS=Q/T


The Attempt at a Solution



The real issue I'm having is how to go about solving this, I think I'm going to need to use kinematics to find the time the gold is exposed to the air correct? but then I'm not sure how to use that time value or anything. My book has no problems like this. Any and all guidance will be greatly appreciated.
 

Attachments

  • x2,1.JPG
    x2,1.JPG
    14.4 KB · Views: 549
Physics news on Phys.org
physninj said:

Homework Statement


http://postimage.org/image/9artvc1h5/ see attached

Homework Equations


ΔS=Q/T

The Attempt at a Solution



The real issue I'm having is how to go about solving this, I think I'm going to need to use kinematics to find the time the gold is exposed to the air correct? but then I'm not sure how to use that time value or anything. My book has no problems like this. Any and all guidance will be greatly appreciated.
You do not have to worry about the time the gold is exposed to the air. You just need to know the total heat flow into the surroundings.

When everything reaches equilibrium, has the temperature of the air or ice changed? So if you know the amount of heat flow into the surroundings, what is its change in entropy?

What is the heat flow into the surroundings generated by the cooling of the gold? (hint: you need an expression for ΔQ as a function of ΔT).

What is the change in entropy of the gold? (hint: ΔS = ∫dQrev/T).

What is the heat flow into the surroundings generated by the kinetic energy of the gold? Assume that energy is absorbed by the ice and air.

What is the total amount of heat flow into surroundings? So what is the change in entropy (hint: that part is easy).

Add the changes in entropy together.

AM
 
Last edited by a moderator:
So I calculated the Q for the gold to reach -20 degrees using the specific heat of gold (wasn't provided for practice test??), I'm not sure if that's the right move. I assume because the surroundings are at -20 that there is no real change in the temp of the air and ice overall, otherwise I wouldn't know what to do.

Q=m(spH)ΔT

Q=(1500 g)(.126 J/gK)(-20-1500)= -287280 J

For the entropy change of the gold

ΔS=∫dQ/T=c∫dT/T=(m(spH))ln(T2/T1)=(189)ln(253/1773)= -367.99 J/K

Now, when you say kinetic energy of the gold, do you mean from its speed falling? If so I used the change in gravitational potential to calculate that part. I don't know if I can just say its Q2 but yeah.

ΔUg=mghf-mghi=0-(1.5 kg)(9.8 m/s^2)(150 m)=-2205 J=Q2??

total heat flow into surroundings 289485 J

change in entropy of surroundings ΔS=Q/T=(289485 J)/(253 K)= 1144.21 J/K

adding changes in entropy gives 776.219 J/K, is this change in entropy of the universe then?

Not very confident in all of this so please let me know wherre I'm wrong. Thank you :)
 
Does my work look alright? I don't want to let the thread die quite yet. If it goes down again I suppose I can take it to mean I'm all good.
 
physninj said:
Does my work look alright? I don't want to let the thread die quite yet. If it goes down again I suppose I can take it to mean I'm all good.
Everything looks good and is well explained. Well done.

AM
 
Thank you very much for your help.

For reference I believe I forgot a piece, the latent heat of fusion for the gold which solidifies at 1064 °C

Q_fusion=-m*Lh=-(1.5 kg)(63000 j/kg)= -94500 J
ΔS=Q/T=-94500/(1064+273)= -70.68 J/K

Making total change in entropy of the gold -438.67 J/K

making heat flow into surroundings 383985 J and entropy change 1517.727 J/K

change in entropy of universe becomes 1079.057 J/K
 
Last edited:
physninj said:
Thank you very much for your help.

For reference I believe I forgot a piece, the latent heat of fusion for the gold which solidifies at 1064 °C

Q_fusion=-m*Lh=-(1.5 kg)(63000 j/kg)= -94500 J
ΔS=Q/T=-94500/(1064+273)= -70.68 J/K

Making total change in entropy of the gold -438.67 J/K

making heat flow into surroundings 383985 J and entropy change 1517.727 J/K

change in entropy of universe becomes 1079.057 J/K
You are thinking! Since the gold is a liquid at 1500C you might want to check the heat capacity for liquid gold as it may be higher than for solid gold - not that it will make a huge difference here.

AM
 

Similar threads

Thermodynamics: I can't solve this simple entropy exercise....
  • · Replies 1 ·
Replies
1
Views
1K
Change in temperature for a system with entropy change
  • · Replies 4 ·
Replies
4
Views
2K
Entropy - show positive net entropy change....
  • · Replies 23 ·
Replies
23
Views
4K
Calculus problem regarding Thermodynamics HW (entropy for C2H5OH at 348K)
  • · Replies 2 ·
Replies
2
Views
1K
Change in entropy of an ideal gas during thermodynamic cycle
  • · Replies 1 ·
Replies
1
Views
2K
Solve Entropy Gen of Water-Ice Contact, 100J Transferred
  • · Replies 3 ·
Replies
3
Views
2K
Finding Isentropic Enthelpy, knowing Isentropic Entropy
  • · Replies 3 ·
Replies
3
Views
2K
Computing entropy change of ideal gas during heating
  • · Replies 8 ·
Replies
8
Views
2K
How to calculate the entropy for two sources
  • · Replies 5 ·
Replies
5
Views
2K
Entropy Change of Touching Blocks That Reach Equillibrium
  • · Replies 7 ·
Replies
7
Views
6K