Mass ratio of steam-ice mixture

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SUMMARY

The discussion focuses on calculating the mass ratio of an ice cube at 0 degrees Celsius mixed with steam at 100 degrees Celsius, both reaching equilibrium at 50 degrees Celsius. The correct mass ratio of ice to steam is established as 4.5:1, contrary to an initial incorrect calculation of 6.8:1. Key equations used include Q=ml for latent heat and Q=mcdT for temperature changes. Participants emphasize the importance of balancing energy transfers between the melting ice and condensing steam to arrive at the correct ratio.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically energy conservation.
  • Familiarity with latent heat calculations (Q=ml).
  • Knowledge of specific heat capacity (Q=mcdT).
  • Basic algebra for solving equations and ratios.
NEXT STEPS
  • Study the principles of energy conservation in phase changes.
  • Learn about specific heat capacity and its application in thermal calculations.
  • Practice problems involving latent heat and temperature changes in mixtures.
  • Explore detailed examples of energy balance in thermodynamic systems.
USEFUL FOR

Students studying thermodynamics, physics educators, and anyone interested in understanding energy transfer in phase changes involving water.

Aaronkwg
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Homework Statement


Ice cube at 0 degree is mixed with steam at 100 degree, both become water at 50 degree.
Find the ratio of mass of the ice : mass of steam

Homework Equations



Q=ml
Q=mcdT

The Attempt at a Solution


I tried this way :
let the ratio of ice to steam = a:b
a x 3.34x10^5=b x 2.26x10^6
and i found out it was 6.8:1, but the answer is 4.5:1
I have no idea.
Thx in advance!
 
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you are ignoring the temperature changes. the ice melts to water at 0C and steam condenses to water at 100C, but then they come to equilibrium at 50C.
 
So should i add the 4200x50xa and 4200x50xb?
But I still get it wrong.
 
basically you need to balance the energy; any energy that comes out one system goes into the other. so, on one side of the equation, you should record all the energy it takes to melt, and then raise the temperature of, the ice/water. on the other side, record the energy to condense, and then lower the temperature of, the steam/water. you seem to have all of the terms correct, and when i use your numbers i get 4.5:1 as well, so maybe check your arithmetic.

it would help if you put up all of your work: for instance 4200x50xa is the energy needed to raise the temperature of the water that was ice, but it is not clear how you used that to make your calculations.
 

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