How Much Energy Is Required to Convert Ice at -13°C to Steam at 113°C?

[Aikenfan]

Given:

cp, ice = 2090 J/ kg . Celsius
cp, water = 4186 J/ kg . Celsius
cp, steam = 2010 J/ kg . Celsius
Lf = 3.33 x 10 ^5 J/ kg
Lf = 2.26 x 10 ^6 J/ kg

How much energy is required to change a 38g ice cube from ice at -13 degrees C to steam at 113 degrees C? Answer in units of J.

I know thAt the formula (m)(c)(change in T) is going to be used but i don't know where to start. please help! thank you

 

[AndreJ]

The specific heat formula is indeed, mc$$\Delta$$T, where m=mass, c=specific heat capacity and $$\Delta$$T= change in temperature.

You'll need to find what energy is required in each transformation, from ice->water then water->steam, using the different specific heat capacities. The answer should be the sum of the 2 energy amounts.

That's what I think it would be, but someone else might want to confirm/deny this.

At least, that will give you a starting position :).

 

[mjsd]

yes you will need the latent heat for phase transformation... are the Lf 's in the data given meant to be them?... dimensionally they are correct for being the latent heat value (note: the unit is just J/Kg and not J/(Kg.C))...remember during phase transformation there is no termperature change...

 

[AndreJ]

yes you will need the latent heat for phase transformation... are the Lf 's in the data given meant to be them?... dimensionally they are correct for being the latent heat value (note: the unit is just J/Kg and not J/(Kg.C))...remember during phase transformation there is no termperature change...

Does that mean that, during phase change the energy will be a constant amount, or will it still change with change in specific heat capacity (as I thought it was)?

 

[AngeloG]

You need to see a graph of the phase change and how it works =). Then for each, label each step as it goes through.

Then apply the ideas behind thermodynamics and energy. (Q, W, U etc.)

It looks similar to this (Pulled it off a website):
http://upload.wikimedia.org/wikibooks/en/1/15/Graph1.jpg

Depending on what's happening you will use latent heat of fusion or vaporization =). First draw what's happening and the path you are taking on the graph.

*NOTE* Each flat part of the graph is a phase change =).

 

[mjsd]

Does that mean that, during phase change the energy will be a constant amount, or will it still change with change in specific heat capacity (as I thought it was)?

not sure what you mean by this, but the picture is as follow:
you need energy to first change termperature from a negative value to 0 (melting point) and this require energy... the energy is given by
$$E_{\text{to melting point}}= \text{mass of substance} \times \text{sepcific heat of substance in that state} \times \text{change in temperature}$$

then phase change requires energy (say break up crystallise structure or inter-molecular bonds),,... temperature doesn't change during this period for we assume that all energy is solely used up by phase change only. so you get

$$E_{\text{ice to water}}= \text{mass of substance} \times \text{latent heat of substance for going from state 1 to state 2}$$

Then once it is water the specific heat of water comes in... etc.
remember specific heat is simply a measure of how hard it is too change the temperature of a substance of a given mass by say 1 deg while latent heat is a measure of how hard to change a substance of a given mass from state 1 to state 2.