Mass ratio of steam-ice mixture

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Homework Help Overview

The problem involves a thermal interaction between an ice cube at 0 degrees Celsius and steam at 100 degrees Celsius, resulting in both substances reaching thermal equilibrium at 50 degrees Celsius. The goal is to determine the mass ratio of the ice to the steam.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the energy balance required for the phase changes and temperature adjustments of both the ice and steam. There are attempts to set up equations based on energy conservation, with some questioning the treatment of temperature changes and the arithmetic involved in the calculations.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the energy balance. Some guidance has been provided regarding the need to account for all energy changes involved in melting and heating the ice, as well as condensing and cooling the steam. There is no explicit consensus on the correct approach yet.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the information available for discussion. There is a noted discrepancy between the calculated mass ratio and the expected answer, prompting further investigation into the assumptions and calculations made.

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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