A design for purifying helium consists of an adiabatic process that splits a helium stream containing 30 mole% methane into two product steams, one containing 97 mole% helium and the other containing 90 mole% methane. The feed enters the process at 10 bar and 117oC. The methane-rich product leaves at 1 bar and 27oC while the helium-rich product leaves at 50oC and 15 bar. The process produces work! Assuming He is an ideal gas with CP = (5/2) R and methane is an ideal gas with CP = (9/2) R, calculate the total entropy change of the universe for the process on the basis of 1 mole of feed in order to determine whether the process violates the 2nd Law.
Hints :
The first step in the analysis of this process is to solve the material and energy balance equations. The more subtle part is to calculate ΔS for the process. I broke the process into a hypothetical process path consisting of seven steps. Three of these steps consist of mixing pure He and CH4 at constant T and P while the remaining four steps involved changes in T or P for either pure He or CH4.
4 comments:
A student asked me about Wshaft in thes problem. He wrote:
"I notice that you give a solution for Wshaft in the problem set for problem number 2. The problem statement does not ask us to calculate work shaft, only deltaS for the process and determine whether the process violates the second law. Do you want us to calculate Wshaft?"
I replied:
"It was claimed that the proposed process not only splits the He/Ch4 mixture, but also produces work. I applied the 1st Law to see if this was possible. It is. The process could produce almost 2000 J of work !"
Yes, you should calculate Wshaft.
So when calculating the Entropy change for mixing/unmixing, is the entropy change for mixing the negative for the theoretical unmixing entropy change?
trump=5 9:16 PM:
Yes. The key here is to compute the total entropy change...NOT the molar entropy change.
So, the deltaS for mixing 2 moles of N2 with 3 moles of Ar is the negative of the deltaS to unmix 5 moles of the mixture in to 2 moles of pure N2 and 3 moles of pure Ar.
Good question !
Please open GOOgle and klick metozor and after : index of metozor At is site that explains technical details in easy to understand language. example : http://www.nets.pl/~metozor/for_greenpeace.html or
http://www.nets.pl/~metozor/energy_for_everybody.html
Everyone is able to build just the model of METOZ machine and test it. Please, have a look at http://www.nets.pl/~metozor/supplement.html Perhaps METOZ is some duplicating machine of a clean energy.
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