Specific/Latent Heat and Melting Iron

[Anony-mouse]

Homework Statement

How much heat is needed to melt 16.7 kg of iron that is initially at 21.3°C?

Homework Equations

Q=m*c*ΔT + mL

The Attempt at a Solution

here: m=16.7kg, c=0.45kJ/kg*K, and ΔT=1538-21.3=1516.7

Thus, Q1=1.14e7 J

Then, I need to calculate latent heat needed, which is Q2 = (2.67 x 10^5)* (16.7) = 0.44584 x 10^7

So, the total heat needed is: Q1+Q2=1.55x10^7 J. I also got 1.58x10^7 on my second try.

But neither are the right answer. What did I do wrong?

 

[rock.freak667]

Homework Statement

How much heat is needed to melt 16.7 kg of iron that is initially at 21.3°C?

Homework Equations

Q=m*c*ΔT + mL

The Attempt at a Solution

here: m=16.7kg, c=0.45kJ/kg*K, and ΔT=1538-21.3=1516.7

Thus, Q1=1.14e7 J

Then, I need to calculate latent heat needed, which is Q2 = (2.67 x 10^5)* (16.7) = 0.44584 x 10^7

So, the total heat needed is: Q1+Q2=1.55x10^7 J. I also got 1.58x10^7 on my second try.

But neither are the right answer. What did I do wrong?

I think Q1 is 1.14e4 J (according to my calculator).

But I found like 3 values for the latent heat of iron

Iron, gray cast 96 kJ/kg
Iron, white cast 138 kJ/kg
Iron, slag 209 kJ/kg


So not too sure which one is correct for the question.

 

[Borek]

I think Q1 is 1.14e4 J (according to my calculator).

J or kJ?

 

[rock.freak667]

J or kJ?

ah didn't notice the units of c...but I'd still get the OP's answer for the 2nd try using that value of the latent heat.