Efficiently Manufacture 3.0kg of Ice Cubes: Calculating Minimum Work

  • Thread starter Thread starter CartoonKid
  • Start date Start date
  • Tags Tags
    Ice Manufacturing
Click For Summary
SUMMARY

The discussion focuses on calculating the minimum work required to manufacture 3.0kg of ice cubes from water at 0°C, with surroundings at 30°C. The latent heat of fusion for water is specified as 338.7 kJ/kg. The initial calculations yielded varying results, with one participant concluding 111.7 kJ as the correct work required, while others provided different figures. The efficiency of the process was calculated to be approximately 9.9%, which is critical for determining the input work needed based on the Carnot cycle principles.

PREREQUISITES
  • Understanding of thermodynamics, specifically the Carnot cycle
  • Knowledge of latent heat of fusion
  • Familiarity with efficiency calculations in thermodynamic systems
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the Carnot cycle and its implications on efficiency
  • Learn about the latent heat of fusion and its applications in phase changes
  • Explore the concept of Coefficient of Performance (COP) in refrigeration cycles
  • Investigate the relationship between temperature, work, and energy in thermodynamic processes
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, mechanical engineers, and anyone involved in refrigeration or energy efficiency calculations.

CartoonKid
Messages
125
Reaction score
0
Calculate the minimum work required to manufacture 3.0kg of ice cubes from water initially at 0C. Assume that the surroundings are at 30C. The latent heat of fusion of water at 0C is 338.7kJ/kg.

My working:
[tex]e=1-\frac{273}{303}[/tex]
then
[tex]e=\frac{work}{input}[/tex]
[tex]input=(3.0)(338.7E3)[/tex]
[tex]work=100.6kJ[/tex]

But I saw the other answer from someone that it is 117.1kJ. Which one is the correct answer? Is my answer correct? If not, please rectify for me. Thanks.
 
Physics news on Phys.org
First of all efficiency=1-T2/T1*100%=1-273/303*100%=9.9%
Then efficiency=usefuloutput/Inputbythemachine=(3*338700)/input
So
work needed as I calculated is 102.64KJ AND you are both wrong (if I am not wrong...)
Thats because what you have to calculate is the input the machine needs since it has the given efficiency to make it out to create ice cubes or whatever...
 
Now I have got the way of how the other answer was being worked out.
[tex]COP=\frac{Q_{cold}}{Work}[/tex]
[tex]COP=\frac{T_{cold}}{T_{hot}-T_{cold}}[/tex]
After sub in all the values,
[tex]Work=\frac{(3.0)(338.7E3)}{9.1}[/tex]
and the answer appears to be 111.7kJ (sorry, typo error in the first post)
ColdRifle, I don't understand why you sub in (3.0)(338.7E3) as your usefuloutput. Isn't that eff=work/input for carnot cycle?
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
7
Views
3K
Replies
1
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
6K