Interpretation :
An air stream with conditions
Concept Introduction :
A thermodynamic process is possible if and only if it follows laws of
According to the first law of thermodynamics the energy or enthalpy of the universe is constant or conserved and it can convert from one form into another form and hence
According to the second law of thermodynamics process is process if and only if the total entropy (system surrounding) is greater than or equal to zero for any change of state of the system. Hence,
And formula for entropy generation in steady state flow process with one input stream is
And for the Hilsch vortex tube, considering adiabatic vortex tube
And for an ideal gas
Answer to Problem 5.46P
Process is valid with values
Explanation of Solution
Given information:
It is given that Hilsch vortex tube operates with no
Hence
The mass flow rate of warm air leaving is six times that of the cool air mass flow rate.
It is given that air is assumed to be an ideal gas at the conditions given.
Basis:
Hence
Mass flow rate of warm air leaving is six times that of the cool air mass flow rate i.e.
Therefore, the mass fraction of the cooler air in the output stream of air is
And mass fraction of warm air stream in the output is
Hence
Total enthalpy change of the output stream is:
And we know that for an ideal gas,
Thus,
Where
And
For warmer air stream
Values of above constants for air in equation (1) are given in appendix C table C.1 and noted down below:
Hence
And
And for cooler air stream
And
Hence Total energy change during the process is
Hence it is nearly zero and has finite value. So, first law of thermodynamics is valid.
Now, Total entropy change of the output stream is:
And we know that for an ideal gas,
Thus,
Where
And
For warmer air stream
Values of above constants for air in equation (1) are given in appendix C table C.1 and noted down below:
Hence
And
And for cooler air stream
And
Hence Total entropy change during the process is
Hence
Hence total entropy (system surrounding) is greater than or equal to zero for any change of state of the system. So, second law of thermodynamics is valid.
So, we can say that both first and second law of thermodynamics are valid for the given process hence this process is possible.
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Chapter 5 Solutions
Introduction to Chemical Engineering Thermodynamics
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