A gas stream is entering a separator at 1 mole/sec with mole fractions 15% A and

Question

A gas stream is entering a separator at 1 mole/sec with mole fractions 15% A and 85% B. (Component 1 is A, component 2 is B.) At surface, the gas stream is 8 bar and 350K. Two streams exit the separator, one primarily of A (0.99 A1, 0.01 A2), and one of primarily B (0.01B1, 0.99B2). Work can be inputted or output from the separator, but not heat. Both exit gas streams are at 8 bar and at the same temperature (T2, which may be different than the input temperature, T1). Assume the mixture is an ideal gas mixture, and the heat capacity for both A and B is 37 J/mol-K. Calculate the flow rates in moles/sec of the two exit streams. If the separator is operating at maximum efficiency, is work output from the separator, or is work inputted? Explain. Now, calculate the temperature of the output streams if the separator is at maximum efficiency.

Explanation / Answer

We will use the relation,

PV = nRT

For A the flow rate is, V = nRT/P

With n = 0.15; P = 8 bar = 7.9 atm; T = 350 K

We have,

V (A) = (0.15 x 0.0821 x 350) / 7.9

   = 0.55

Flow rate of B with n = 0.85, P, T remains the same, we have,

V (B) = 0.85 x 0.0821 x 350 / 7.9

         = 3.10

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