# Heat Energy Required

1. May 11, 2013

### kingstar

1. The problem statement, all variables and given/known data
Calculate the heat energy required to convert 0.1 kg of ice at -30°C into water at 0°C. The
specific heat capacity of ice is 2100 J kg-1K-1
and the latent heat of fusion of ice is 3.25 x 10^5 J kg-1

2. Relevant equations

e=mcθ

3. The attempt at a solution

So first i did
e = 0.1 x 2000 x 30 = 6300.

I'm sure I am missing something because I havent used the latent heat of fusion of Ice? and I'm not sure why i would need that :S

2. May 11, 2013

### rock.freak667

You will need to get the energy required to heat the ice from -30 to 0 + energy required to change the ice to water (this is where the latent heat comes in)

3. May 11, 2013

### CWatters

There are two steps..

1) Heat required to warm the ice from -30 to 0C. This depends on the Specific Heat Capacity of ice. You were correct except for the typo and missing units..

2) Heat required for the phase change (eg to melt the ice to water) while it remains at 0C. This depends on the Latent heat of fusion of ice/water which is ..

= 0.1 x 3.25 x 10^5 = 32500 Joules.

Aside: The Latent heat of fusion and Latent heat of vapourisation of water are quite high. One reason why steam is dangerous is that a heck of a lot of energy is given out when the steam condenses to water on your skin. The heat given out by steam condensing is roughly 10 times that given out when the resulting water cools from say 100C to body temperature.

4. May 11, 2013

### kingstar

Ahhhhhhhh thanks
i forgot the phase change completely!

Makes sense now, thank you!