# Homework Help: Gallons of H20 needed to cool molten steel

1. Jul 29, 2013

### tconlon33

I am trying to figure out how much water (gallons) would be needed to cool 1 ton of molten Carbon Steel from 2200F to 212F. The specific heat of Carbon Steel is 0.49 Kj/kg.C

I am not sure where to start. I tried used Newtons Law of Cooling but I dont think this is the place to start.

After some reading, I multiplied the mass x specific heat × ΔTemp. I kind of understand that from here I need to do somthing with steam/water enthalpy. I am far removed from Physics class but am trying to figure this out for my internship. Any help whatsoever would be very appreciated. Thanks for you time and have a great day all.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 29, 2013

### voko

At 2200 F steel is no longer liquid, so saying "molten" should be avoided.

Are there any restrictions on how you can conduct cooling? For example, you can take a small amount of very cold water, then the steel will heat it to boiling, evaporate it, then it will heat the steam to a very high temperature, then you can vent the steam. Doing this gradually, you will reduce the temperature of steel to 212 F. Or you can just take a very large - infinitely large, in fact - amount of water already at 212 F. Obviously, it takes different amounts of water to achieve the same effect in these two cases.

3. Jul 29, 2013

### SteamKing

Staff Emeritus
It's also going to depend on how much surface area the hot steel will present for cooling. Obviously, a ton of hot steel in a cubical shape will retain heat longer than if the steel is rolled out into a long slab.

Also, I wouldn't worry too much about heat transfer to any steam produced when water hits the hot metal. Unless the steel is put into a closed chamber which can contain any steam generated, any steam produced is going to rise from the hot surface and not be available for any additional heat transfer (at least by conduction; radiation from the hot steel is another matter). In any event, steam has a much lower heat capacity that liquid water.

At high temperatures, there will be some heat loss from the steel due to radiation. This is somewhat harder to evaluate than merely dumping a lot of cold water onto hot steel.

Although this may seem to be a simple problem on first inspection, it has quite a bit of nuance to consider.

4. Jul 29, 2013

### Bandarigoda

Well i think you can use,
E = mc¤

5. Jul 29, 2013

### CWatters

That will give you a figure for the energy that has to be removed from the steel into the water.

212F = 100C the boiling point of water so we could assume that water is sprayed onto the hot steel turning all the water into steam (after which the steam is vented outside the plant?). In which case the amount of energy going into the water would be made of two components...

1) Energy required to heat the water from say 25C to 100C is....

= Mwater * SHCwater * (100-25)

2) Energy required to change the water at 100C to steam at 100C

= Mwater * LHwater

where:

Mwater = mass of water (currently the unknown)

LHwater is the Latent Heat of Vaporization (aka boiling)...

http://www.britannica.com/EBchecked/topic/331406/latent-heat
https://en.wikipedia.org/wiki/Latent_heat

Component 2) will be much larger than component 1) so you could even ignore 1).

Anyway for completeness add these two together...

Esteam = {Mwater * SHCwater * (100-25)} + {Mwater * LHwater}

Equate that to the amount of energy that has to be removed from the steel and solve for the mass of water.

6. Jul 29, 2013

### tconlon33

H20 cooling of Steel

Thanks for all of the advice. I am far better off than I was before. To clarify some things, the water that is being used is around 60-80F before application. The actual application that this is for, is when the "Slag" or byproduct from steel production is dumped into yards or pits, it is in mostly molten form. Since their is no specific heat available for slag, I just used the SH for carbon steel because this is pretty close to the product. The surface area varies so I cannot really give a good awnser to that question brecause the product is dumped and the viscosisty and consistancy is always varying.

7. Jul 29, 2013

### voko

I am no expert in metallurgy, but I find it dubious that the heat capacity of slags is pretty close to steel. Moreover, if the slags are liquid when they are dumped, you need to take into account their heat of fusion.

8. Jul 29, 2013

### tconlon33

This is a general formula I am trying to figure out. A rough gallons per ton estimate. I know that it is going to be far from exacty but the actual industry doesnt exactly work in a precise manner. Slag has a similar heat capacity to steel because IT IS steel, just the "leftover" metals from a certain process that are drained from the bottom of the "barrel" per say before the steel is rolled or put into whatever shape its going to. I am honestly looking for just a rough estimate. The actual water is sprayed on with hoses similar to firehouses but with much less pressure. The pits are also flooded from time to time

9. Jul 29, 2013

### voko

A rough estimate would just use the heat of vaporization of water and ignore its heat capacity.

However, I am really curious at this stage as to why you think slag is steel. To the best of my knowledge, slags are mixtures of compounds such as oxides and sulfides.

10. Jul 29, 2013

### tconlon33

Your right, it is not simply steel like I said. It is mostly oxides and sulfides but many of the plants that we work at (we dont make the steel, we recover the slag), have a high amount of steel left in because of quality issues and other. I probably would have tried to find a different specfic heat that more accuratly reflects the actual composition but for time constraints I have been told to just use the specific heat of carbon steel. I know it doesnt make that much sense, just doing what i am told. You are definately right about slag though.