Minimum work to separate O2 &N2 from air

In summary, the question provides the composition of air at 25C and 100kPa, with mole fractions of 0.7567 for nitrogen, 0.2035 for oxygen, 0.0303 for water vapor, and 0.0003 for carbon dioxide. The question then asks for the minimum work required to separate 1 kmol of oxygen and 1 kmol of nitrogen from the atmosphere at the given conditions. The solution involves calculating the entropy change for the mixing process and assuming air is composed of only oxygen and nitrogen. However, it is not specified how much air should be initially present, which may affect the final answer.
  • #1
obscure
8
0
1. assume air is an iseal gas at 25C and 100kPa. the mole fractions of components are nitrogen_0.7567
oxygen=0.2035 water vapor=0.0303 carbon dioxide=0.0003 Calc. min work to seperate
a-1kmol O2 at 25C 100kPa
b-1kmol N2 at 25C 100kPa from atmosphere

Homework Equations


Wmin=ge-gi=(ho-To.se)-(hi-To.si) [/B]

The Attempt at a Solution


for ideal gas Wmin=To(si-se)=-R.To. total(Xi.lnxi)
I assume air is composed of only O2 and N2, min ork is equal to - of the entropy change for mixing process
but Iam confused it is asked only to separate 1 kmol O2[/B]
 
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  • #2
obscure said:
a-1kmol O2 at 25C 100kPa
b-1kmol N2 at 25C 100kPa
One kmol O2 and one kmol N2.
 
  • #3
Bystander said:
One kmol O2 and one kmol N2.
1 kmol of oxygen at 25C and 100kPa and
1 kmol of nitrogenat 25C and 100kPa from atmosphere
 
  • #4
obscure said:
3. The Attempt at a Solution
for ideal gas Wmin=To(si-se)=-R.To. total(Xi.lnxi)
I assume air is composed of only O2 and N2, min ork is equal to - of the entropy change for mixing process
but Iam confused it is asked only to separate 1 kmol O2
Why do you assume that? It gives the composition, and it includes water vapour and CO2.
Why does the question confuse you?
The thing that is not clear to me is how much air you should start with. Perhaps the answer tends to a limit as the initial number of moles tends to infinity.
 
  • #5
Bystander said:
One kmol O2 and one kmol N2.
Yes, but not from the same air sample. They are presented as two independent questions.
 

Related to Minimum work to separate O2 &N2 from air

1. How is the minimum work to separate O2 & N2 from air calculated?

The minimum work to separate O2 and N2 from air is calculated using the Second Law of Thermodynamics and the principle of maximum work. This involves taking into account the thermodynamic properties of the components of air, such as their boiling points and heat capacities, and the efficiency of the separation process.

2. What methods are commonly used to separate O2 & N2 from air?

The most commonly used methods for separating O2 and N2 from air are cryogenic distillation, pressure swing adsorption, and membrane separation. Each method utilizes the different physical properties of the components of air to achieve separation.

3. How does the purity of O2 and N2 affect the minimum work required for separation?

The purity of O2 and N2 in the air affects the minimum work required for separation. The higher the desired purity of the separated components, the more work is required. This is because the separation process becomes more energy-intensive as the concentration of the desired component decreases.

4. Can the minimum work to separate O2 and N2 from air be reduced?

The minimum work required for separation can be reduced by increasing the efficiency of the separation process, improving the design of the equipment used, and optimizing the operating conditions. Advances in technology also play a role in reducing the minimum work required for separation.

5. What are the applications of separating O2 and N2 from air?

The separation of O2 and N2 from air has a wide range of applications, including in the production of medical-grade oxygen, industrial gas separation, and in the production of high-purity nitrogen for use in electronics and food packaging. It is also used in the production of liquid oxygen and nitrogen for rocket fuel and in the steel industry for oxygen enrichment.

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