(adsbygoogle = window.adsbygoogle || []).push({}); I need to calculate q, w, [tex]\Delta E[/tex], [tex]\Delta H[/tex] and [tex]\Delta S[/tex] for the process of heating a sample of ice weighing 18.02 g (1 mole) from -30.0 °C to 140.0°C at constant pressure of 1 atm.

Given are the temperature independent heat capacities (C_{p}) for solid, liquid and gaseous water: 37.5 J/K/mol, 75.3 J/K/mol, 36.4 J/K/mol respectively. Also, the enthalpies of fusion and vaporization are 6.01 kJ/mol and 40.7 kJ/mol respectively. Assure ideal gas behavior.

I thought of this process as 5 steps:

I) Solid water of -30°C is heated to 0°C

II) Solid water of 0°C melts to give liquid water at 0°C

III) Liquid water of 0°C is heated to 100°C

IV) Liquid water of 100°C is vaporized to give gaseous water at 100°C

V) Gaseous water of 100°C is heated to 140°C

Then I figured I needed to calculate q, w, [tex]\Delta E[/tex], [tex]\Delta H[/tex] and [tex]\Delta S[/tex] for each step seperately and sum them to give the values of q, w, [tex]\Delta E[/tex], [tex]\Delta H[/tex] and [tex]\Delta S[/tex] for the whole process.

=> So q is calculated for I),III) and V) by q=n C_{p}[tex]\Delta T[/tex] with the C_{p}values of respectively solid, liquid and gaseous water. For II) and IV) q= n H with values of H of respectively fusion and vaporization enthalpies.

=> Because the process is carried out at constant pressure, all the q's equal the H's.

=> Entropies are calculated for I), III) and V) by [tex]\Delta S = n C_p ln \frac{T_2}{T_1}[/tex] and for II) and IV) with [tex]\Delta S =\frac{\Delta H}{T}[/tex] with T the melting/boiling point and delta H the fusion/ vaporization enthalpy.

=> Now the point at which I got stuck: calculating w and [tex]\Delta E[/tex]

I know that [tex]\Delta E = w + q [/tex] and [tex]w = -p \Delta V[/tex]. For V) I can calculate w with p= 1 atm and by using the ideal gas law to find delta V and with the delta E formula + known q delta E can be obtained.........

But what about the work that is done in the other four steps? I don't know the changes in volume. Could somebody please please please explain to me how I'd calculate w and delta E for the first 4 steps?

EDIT: Now I figured delta E = 0 for II and IV therefore w=-q, because [tex]\Delta E = n C_v \Delta T [/tex] thus it only depends on the temperature, which remains constant during II and IV, so [tex]\Delta T =0 = \Delta E[/tex] . Is that a correct way of thinking? And now how would I tackle calculation of delta E & w of step I, III and V?

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# Thermodynamics: calculate q, w, E,H,S for a 5 step process

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