Control volume, steady- state and steady-flow devices, enthelpy

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Discussion Overview

The discussion revolves around a homework problem involving the compression of air, focusing on the application of the first law of thermodynamics, enthalpy, and the assumptions regarding air as an ideal gas. Participants are exploring the calculations needed to determine the power input required for a specified mass flow rate during the compression process.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a calculation for the power input required during the compression of air, applying the first law of thermodynamics and assuming certain values for specific heats.
  • Another participant challenges the application of the first law as presented, arguing that enthalpy is not conserved in this scenario and suggesting a different formulation of the first law involving internal energy.
  • A subsequent participant inquires about how to approach the problem if air is considered an ideal gas, indicating a need for clarification on the assumptions involved.
  • Further discussion emphasizes the need to consider changes in internal energy and heat, suggesting a more detailed examination of the first law in the context of the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct application of the first law of thermodynamics in this context. There are competing views on how to approach the problem, particularly regarding the treatment of enthalpy and the assumptions about air as an ideal gas.

Contextual Notes

Participants express uncertainty regarding the applicability of the first law in its traditional form, particularly in relation to the non-constant pressure conditions of the compression process. There are unresolved questions about the assumptions made in the initial calculations and the implications of treating air as an ideal gas.

Aeronautical1
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Homework Statement



Air is to be compressed from 120 kPa and 310 K to 700 kPa and 430 K. A heat loss of 20 kj/kg occurs during the compression process. For air: cv=0.7165 kj/kg.K and R=0.287 kj/kg.K .

A) Neglecting kinetic energy changes determine the power input required for a mass flow rate of 90 kg/min.


The Attempt at a Solution



m = 90 kg/min = 1.5kg/s

Apply 1st law of thermodynamics - energy conservation

Ein = Eout

Win + Mh1 = Qout + mh2

Therefore:

Win + mCpT1 = Qout + mCpT2

Cp = 1.005 Kj/Kg.K

Win + 1.5kg X 1.005 KJ/Kg.K X 310K = 20KJ/Kg/K + 1.5Kg/s X 1.005 KJ/Kg.K X 430K=

Win = 201Kw.


Is this correct?
 
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Aeronautical1 said:
1. Apply 1st law of thermodynamics - energy conservation

Ein = Eout

Win + Mh1 = Qout + mh2

?


What is your justification for this equation? It's not the 1st law. Enthalpy equals heat only at constant pressure, which is not the case here. Or, the other way, enthalpy is not conserved since this is not a throttling process.

How about going back to the real 1st law? U = Q - W

Hint: if the air can be considerd an ideal gas, this problem is trivial. If not, I'm not sure myself how to tackle it at the moment.
 
If air is to be considered and ideal gas here, how would i go about the problem with that in mind?
 
Like I said, start with the first law. What are the changes in U and Q?
 

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