Nitrogen (n2) enters a well-insulated diffuser operating at steady state at 0.656 bar, 300 k with a velocity of 282 m/s. the inlet area is 4.8 x 10-3 m2. at the diffuser exit, the pressure is 0.9 bar and the velocity is 140 m/s. the nitrogen behaves as an ideal gas with k = 1.4. (a) determine the exit temperature, in k, and the exit area, in m2. (b) for a control volume enclosing the diffuser, determine the rate of entropy production, in kw/k.

The exit temperature of the Nitrogen would be 331.4 K.The area at the exit of the diffuser would be .The rate of entropy production would be 0.

Explanation:

First it is assumed that the diffuser works as a isentropic device. A isentropic device is such that the entropy at the inlet is equal that the entropy T the exit.It will be used the subscript 1 for the inlet conditions of the nitrogen, and the subscript 2 for the exit conditions of the nitrogen.It will be called: v the velocity of the nitrogen stream, T the nitrogen temperature, V the volumetric flow of the specific stream, A the area at the inlet or exit of the diffuser and, P the pressure of the nitrogen flow.It is known that for a fluid flowing, its volumetric flow is obtain as: , Then for the inlet of the diffuser: For an ideal gas working in an isentropic process, it follows that: where each variable is defined according with what was presented in step 2 and 3, and k is the heat values relationship, 1.4 for nitrogen.Then solving for , the temperature of the nitrogen at the exit conditions: then, Also, for an ideal gas working in an isentropic process, it follows that:  , where each variable is defined according with what was presented in step 2 and 3, and k is the heat values relationship, 1.4 for nitrogen.Then solving for the volumetric flow at the exit of the diffuser: .Knowing that , it is possible to calculate the area at the exit of the diffuser, using the relationship presented in step 4, and solving for the required parameter: .To determine the rate of entropy production in the diffuser, it is required to do a second law balance (entropy balance) in the control volume of the device. This balance is: , where: and are the entropy of the stream entering and leaving the control volume respectively, is the rate of entropy production and, is the change of entropy of the system.If the diffuser is operating at stable state is assumed then . Applying the entropy balance and solving the rate of entropy generation: .Finally, it was assume that the process is isentropic, it is: , then .

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