Mass of solid water and gaseous water?

[tacloban87]

Homework Statement

a 1kg of Water at 25 degrees celsius is in a container. A solid block of 1kg Carbon Dioxide at its sublimation temp of -80 degrees celcious is placed into the container, with the lid then closed.
Final temperature of entire system = 0 degrees celcius
Final phase of the Carbon Dioxide is gas

*What is the final mass of the liquid H20, solid H20, and gaseous H20?

Homework Equations

Heat of Vap of Water = 2000 kj/kg
Heat of Melt of Water = 300 kj/kg
Csp of Water = 4 kj/kg
Csp of CO2 gas = 1 kj/kg
Heat of Sub of CO2 = 200 kj/kg

[delta]Ethermal = mc[delta]T
[delta]Ebond = ([delta]m)([delta]Heat of...)

The Attempt at a Solution

From what I understand, the H20's conditions change as follows:
Temp Initial = 25 degrees celcius
Temp Final = 0 degrees celcious
Phase Initial = Liquid
Phase Final = Solid

Thus, the H20 will have its thermal energy increasing and its bond energy increasing as well.

As for the CO2's conditions:
Temp Initial = -80 degrees celcius
Temp Final = 0 degrees celcius
Phase Intial = Solid
Phase Final = Gas

Since it is at it's sublimation temperature, it will skip over its intermediate state as a liquid and its thermal energy is increasing and its bond energy decreasing.

So, to find the final mass of the liquid water, do I just use:
[delta]Ethermal = Q
mc[delta]t = Q
(1kg)(4kj/kg K)(0celcius-25celcius) = Q
-100 kj = Q

[delta]m = Q/[delta]Heat of...
[delta]m = -100/300 kg/kg <-- do I use Heat of melting for the liquid phase?

What should be the next step I take in finding the mass of solid water and gaseous water?

 

[Andrew Mason]

Assume that a portion of the H₂O is in the form of liquid. Work out an algebraic formula for the heat flow in terms of the quantity of liquid and solid H₂O. You know that they sum to 1 kg. Use the specific heat of liquid water for the entire mass of H₂O but use the specific heat of fusion only for the portion that ends up as ice.

AM

 

[m2003]

I would suggest using the equations and information provided to calculate the final mass of solid water and gaseous water. To find the final mass of solid water, you can use the formula [delta]m = Q/[delta]Heat of Melt of Water, using the value of 300 kj/kg for the heat of melting. This will give you the change in mass of the water as it goes from liquid to solid form.

For the gaseous water, you can use the formula [delta]m = Q/[delta]Heat of Vap of Water, using the value of 2000 kj/kg for the heat of vaporization. This will give you the change in mass of the water as it goes from liquid to gas form.

Once you have the change in mass for both solid and gaseous water, you can add them to the initial mass of 1kg to find the final mass of each phase. It is important to note that the final mass of solid water may be negative, indicating that some of the solid water has sublimed into gas form.

Additionally, you can use the equation [delta]Ebond = ([delta]m)([delta]Heat of Sub of CO2) to find the change in bond energy for the CO2 as it goes from solid to gas form. This can help you understand the energy transfer that occurs in the system.

Overall, it is important to carefully consider all the equations and information provided in order to accurately calculate the final mass of each phase.