Heat released from condensing steam

[redfire67]

Homework Statement

How many grams of ice at 0 degrees Celsius can be melted by the heat released when one gram of steam condenses to water at 100 degrees Celsius?

Homework Equations

Latent Heat of Fusion of Water: 334 J/g
Latent Heat of Vaporization of Water: 2256 J/g
Specific Heat of Ice: 2.09 J/g degree Celsius
Specific Heat of Water: 4.186 J/g degree Celsius
Specific Heat of Steam: 2.01 J/g degree Celsius

The Attempt at a Solution

First, I tried relating the Lf and the Lv, but I didn't seem to get anywhere. I know that steam condensing to water releases a lot more energy than would water to ice.

Second, I tried factoring in the specific heat of ice, water, and steam, but I'm not sure how those could help me.

Is there some equation that would help me out? Thanks so much for your help.

 

[Hootenanny]

Hi red and welcome to PF,

Firstly, you don't need the specific heats since both phase transitions occur under constant temperature, there is no additional heating/cooling required.

Secondly, do you know how to relate the energy of vaporisation/fusion for a given mass, m (they both obey the same relation). [Hint: If you are stuck, look at the units].

 

[redfire67]

Thanks for the tips, hootenanny.

After going through some more thoughts, I used the latent heats to compare the energy expelled through condensing and the energy gained by melting. If one gram of steam gives off 2256 J condensing and one gram of ice accepts 334 J to melt. Wouldn't it just be 2256J/334J? That would give the amount of mass that that amount of energy would melt, correct?

Hope my logic is correct. Thanks again.

 

[Hootenanny]

Thanks for the tips, hootenanny.

After going through some more thoughts, I used the latent heats to compare the energy expelled through condensing and the energy gained by melting. If one gram of steam gives off 2256 J condensing and one gram of ice accepts 334 J to melt. Wouldn't it just be 2256J/334J? That would give the amount of mass that that amount of energy would melt, correct?

Hope my logic is correct. Thanks again.

Spot on

 

[redfire67]

Thanks for the confirmation.

I have to say I really like this forum. It has helped me many times before even though I haven't registered until now.

Thanks again to all the contributors. You make students like us very happy. ;)

 

[Hootenanny]

Thanks for the confirmation.

No problem

I have to say I really like this forum. It has helped me many times before even though I haven't registered until now.

Thanks again to all the contributors. You make students like us very happy. ;)

Thanks, it's nice to know that our help is appreciated, although we didn't really do much in this case