Thermodynamics ice cube question

[physics_geek]

Homework Statement

How much energy is required to change a 40.0 g ice cube from ice at -8.0°C to steam at 108°C?

Homework Equations

q=mct

The Attempt at a Solution

i remember one of our TAs going over something like this a long time ago..I think i have to like add up all the energies from the ice going to like 0 C then to like 100C and then 108 C??

can someone help me out

 

[astrorob]

Consider the stages that the ice must go through to become water.

Energy is required to raise the temperature, and also to change phases:

http://en.wikipedia.org/wiki/Latent_heat

 

[physics_geek]

ok tell me if I am correct
add up all the energy from ice going from -8 to 0
0 to 100 and then 100 to 108?

am i even close?

 

[astrorob]

Yes, you are. Now you have to also consider the energy required to change phase (ice to water, water to steam).

 

[physics_geek]

umm I am not sure what that means

 

[astrorob]

Consider: http://www.splung.com/heat/images/latentheat/phasechange.png and also the URL I gave you in my first post.

We separate this problem into stages:

Energy is required to raise the temperature of the solid, in this case the ice, from -8 to 0 degrees celsius. This is stage A-B.

Energy is then required to change phase from ice to water. At this point the temperature remains the same. This is stage B-C.

Once again, energy is required to raise the temperature from 0 to 100 degrees celsius. This is stage C-D.

The water then changes state again to steam. This is another phase change. This is stage D-E.

Finally, the temperature of the steam is raised by 8 degrees to 108 degrees celsius. This is stage E-F.

So, to calculate the energy required to raise 40g of ice from -8 to 108 degrees celsius we must use two equations. One to calculate the energy required to change phase at stages B-C and D-E, and another to calculate the energy required to raise the temperature at stages A-B, C-D and E-F.

The latent heat equation is:

$$Q=mL$$

and the other equation required is the one you've already specified.