Calculating Composition & Temp of Mixture After Adding Steam & Ice

[lpp208]

Homework Statement

One kg of steam at 100 degrees Celsius is added to 1 kg of ice at 0 degrees Celsius. What is the composition and temperature of the resulting mixture. The heat of fusion for water is 79.7 kcal/kg, the heat of vaporization is 539 kcal/kg, and specific heats of ice and water are .5 ans 1.0 kcal/kgdegreesC, respectively. Please explain and show all work. Thanks So much.

Homework Equations

q=mc(tfinal-tinitial)

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi lpp208! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[lpp208]

I am stuck on everything. My professor was sick the whole week last week and he basically gave us a take home assignment which we never really got to go over. I am so lost and so I really need help on all of it.

 

[Redbelly98]

Homework Statement

One kg of steam at 100 degrees Celsius is added to 1 kg of ice at 0 degrees Celsius. What is the composition and temperature of the resulting mixture.

Welcome to PF. Let's look at the next two statements:

The heat of fusion for water is 79.7 kcal/kg, ...

Okay, so it takes 79.7 kcal of heat energy to completely melt 1 kg of ice to form liquid water.

...the heat of vaporization is 539 kcal/kg,

That means the 1 kg of steam will give off 539 kcal of heat energy, if all of it condenses into liquid water.

... and specific heats of ice and water are .5 ans 1.0 kcal/kgdegreesC, respectively.

This means that 1 kg of liquid water requires 1.0 kcal of heat energy to heat up by one degree C ... or 100 kcal to heat up 100 degrees C.

... Please explain and show all work. Thanks So much.

Homework Equations

q=mc(tfinal-tinitial)

The Attempt at a Solution

A couple of questions to (hopefully) get you started:

1. How much heat energy does it take to melt the 1.0 kg of ice at 0°C?
2. Where does that energy come from?