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

In summary, 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. requires the calculation of q, w, \Delta E, \Delta H, and \Delta S. The q's are calculated from the heat capacities of solid, liquid, and gaseous water, while the w's and \Delta E's are calculated from the entropies of fusion and vaporization. The \Delta H and \Delta S are then calculated from the entropies and the temperatures.
  • #1
Lisa...
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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 (Cp) 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 Cp[tex]\Delta T[/tex] with the Cp 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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  • #2
Or perhaps it is necessary to calculate w and E directly for the transition (solid) => (gas) with:

[tex]w = -p \Delta V = - n R \Delta T [/tex] and
[tex]\Delta E = \frac{3}{2} R \Delta T [/tex] (=q +w)
and [tex]q= \Delta H = \frac{5}{2} \Delta T[/tex]
 
  • #3
On a second thought, I don't think my edit is such a brilliant idea, because then q= n Cp delta T should be 0 too for step II and IV which can't be cause heat is neaded to melt the ice/vaporize the water.

I know I need densities of -30,0°C ice (solid), 0°C ice/water (solid/liquid), 100°C water (liquid). Then I can calculate delta V for all the steps (the volume of gaseous water can be calculated from the ideal gas law) and thus find w and E... but how would I get that far?
 
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  • #4
Lisa... said:
On a second thought, I don't think my edit is such a brilliant idea, because then q= n Cp delta T should be 0 too for step II and IV which can't be cause heat is neaded to melt the ice/vaporize the water.

I know I need densities of -30,0°C ice (solid), 0°C ice/water (solid/liquid), 100°C water (liquid). Then I can calculate delta V for all the steps (the volume of gaseous water can be calculated from the ideal gas law) and thus find w and E... but how would I get that far?
Since the whole process takes place at constant pressure, do you need to break the process down into steps to find the total PΔV? The ice maybe expands a bit on warming and then melts to become denser water, which first becomes more dense (to 4°C) and then expands and finally evaporates and expands some more, but the total ΔV from start to finish is the difference between the volume of ice at -30°C and the volume of gas at 140°C. The density of ice is reasonably constant at .92g/mL, so the volume is really small compared to the ~22L of gas at the end. I don't think you need to worry about a small uncertainty in ice density.
 
  • #5
Thank you so very very much! :) Now I can finish the problem! You're great :D

Oh btw and I guess that delta E can be calculated with this total work and the TOTAL q right?
 
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  • #6
Lisa... said:
Thank you so very very much! :) Now I can finish the problem! You're great :D

Oh btw and I guess that delta E can be calculated with this total work and the TOTAL q right?

I believe that is correct. Conservation of work/energy. The heat either results in some work being done, or it stays in the system
 

1. What is thermodynamics and why is it important?

Thermodynamics is the branch of physics that studies the relationship between heat, work, energy, and temperature. It is important because it helps us understand and predict how energy is transferred and transformed within a system.

2. What is the purpose of calculating q, w, E, H, and S in a 5 step process?

Calculating these values allows us to quantify the changes in energy, heat, and work that occur during a thermodynamic process. This information is essential in understanding the efficiency and feasibility of a process.

3. How do you calculate q, w, E, H, and S for a 5 step process?

The values for q, w, E, H, and S can be calculated using various thermodynamic equations, such as the first law of thermodynamics and the Gibbs free energy equation. It is important to carefully consider the specific conditions and assumptions of the process before selecting the appropriate equation.

4. What units are typically used for q, w, E, H, and S?

The units used for these values depend on the specific quantities being measured. Q is typically measured in joules or calories, while work is measured in joules. Energy, enthalpy, and entropy can be measured in joules per mole or kilojoules per mole. It is important to pay attention to unit conversions when using thermodynamic equations.

5. How can the values of q, w, E, H, and S be used to analyze a process?

The values of q, w, E, H, and S can be used to determine the efficiency, energy requirements, and feasibility of a process. They can also be used to compare different processes and determine the most efficient or practical option. Additionally, these values can provide insight into the thermodynamic properties and behaviors of a system.

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