Find the Exit Temperature of the Air in the Compressor

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SUMMARY

The discussion focuses on calculating the exit temperature of air in a compressor operating under specified conditions. The compressor has an inlet pressure of 14.7 lbf/in², an inlet temperature of 80°F, and an exit pressure of 90 lbf/in². The heat transfer rate is 9.7 Btu per lb of air, and the power input is 90 hp. The relevant equation for the solution involves the conservation of energy principle, specifically Qcv + m'1(h1 + v21/2) = m'2(h2 + v22/2) + Wcv, where Qcv and Wcv are given values.

PREREQUISITES
  • Understanding of thermodynamics principles, particularly the first law of thermodynamics.
  • Familiarity with ideal gas behavior and properties.
  • Knowledge of energy transfer calculations in mechanical systems.
  • Ability to convert units between horsepower and Btu.
NEXT STEPS
  • Study the first law of thermodynamics and its application to compressors.
  • Learn about ideal gas properties and how to apply them in calculations.
  • Explore energy transfer calculations, focusing on heat transfer and work done.
  • Investigate unit conversions between horsepower and Btu for engineering applications.
USEFUL FOR

Mechanical engineers, thermodynamics students, and professionals involved in compressor design and analysis will benefit from this discussion.

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Homework Statement


Air enters a compressor operating at steady state with a pressure of 14.7 lbf/in2, a temperature of 80°F and a volumetric flow rate of 18 ft3/s. The air exits the compressor at a pressure of 90 lbf/in2. Heat transfer from the compressor to its surroundings occurs at a rate of 9.7 Btu per lb of air flowing. The compressor power input is 90 hp. Neglecting kinetic and potential energy effects and modeling air as an ideal gas, determine the exit temperature in °F.


Homework Equations





The Attempt at a Solution



I suspect that I need to use:

Qcv+m'1(h1+v21/2) = m'2(h2 + v22/2) + Wcv

Is Qcv = 9.7 Btu/lb and Wcv= 90 hp?
 
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