Calculating Heat & Work Done in Ice to Vapour System

[ZeroScope]

I realize that there has been a post recently concerning this sort of thing but i think it went a bit off topic for me to follow. :)
The question is Consider a bowl containing 1 mol of ice at a temperature of -10C and atmospheric pressure. The sample
is heated very slowly to 115C. Split the process into five characteristic phases. How much heat is
consumed and work done during each of the phases? What changes occur in internal energy and in the
Gibbs function during the entire process?

All specific heats are given and latent heats as well as being told to neglect entropy changes apart from during phase transition.

I know the five stages Ice (-10) - Ice (0) - Water (0) etc. and i can work out the amount of heat at each stage using the (mass) . (specific heat) . (Change in temp), and (mass) x (latent heat) for the constant temp. stages. What i don't understand is working out the work done during each phase. I think i need to use U = Q - W and then calculate U and then hence forth calculate W but I am not sure if this is right or even how to do it.

Thanks for any help.

 

[ZeroScope]

sorry just realized that the last part of the question asks for the overall change in internal energy so I am not sure whether my approach holds

 

[pkleinod]

All specific heats are given and latent heats as well as being told to neglect entropy changes apart from during phase transition.

Are you sure? The entropy changes are massive at each stage because you are adding heat. It would be much more sensible to neglect the volume changes except for the phase transitions.

What i don't understand is working out the work done during each phase. I think i need to use U = Q - W and then calculate U and then hence forth calculate W but I am not sure if this is right or even how to do it.

.

Since the pressure is constant, the work done by the system on the surroundings is
just dW = PdV. For the phase transitions, you just calculate the change in volume of the system (here the water or ice) and multiply by the pressure. For the other stages, each
infinitesimal change in temperature, dT, results in work done in the amount
dW =P (dV/dT) dT, so you need to know (dV/dT) for ice, water, and water vapour over the appropriate temperature range of each stage---that is why I suspect you are being told to neglect this, at least in stages 1 and 3. (you know what the volume change is on melting ice and on boiling water, and you know how to estimate this from the equation of state for the gas.)