Find the Exit Temperature of the Air in the Compressor

In summary, the given problem involves a compressor operating at steady state with air entering at 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, with heat transfer occurring at a rate of 9.7 Btu per lb of air flowing. The compressor's power input is 90 hp and kinetic and potential energy effects are neglected, with air modeled as an ideal gas. The task is to determine the exit temperature in °F using the given equations.
  • #1
Northbysouth
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2

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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  • #2
How do you expect to find v?
 

1. How do you calculate the exit temperature of the air in a compressor?

The exit temperature of the air in a compressor can be calculated using the following equation: T_exit = T_inlet * (P_exit/P_inlet)^((gamma-1)/gamma), where T_inlet is the inlet temperature of the air, P_exit is the exit pressure of the air, P_inlet is the inlet pressure of the air, and gamma is the specific heat ratio of the air.

2. What factors can affect the exit temperature of the air in a compressor?

The exit temperature of the air in a compressor can be affected by a variety of factors, such as the inlet temperature and pressure of the air, the compression ratio of the compressor, and the specific heat ratio of the air. Other factors such as ambient temperature, compressor efficiency, and heat transfer can also play a role in determining the exit temperature.

3. How does the specific heat ratio of air impact the exit temperature in a compressor?

The specific heat ratio, also known as the heat capacity ratio, is a measure of how much heat energy a substance can store. In the case of air, a higher specific heat ratio means that the air can absorb more heat energy without experiencing a significant rise in temperature. Therefore, a higher specific heat ratio of air will result in a lower exit temperature in a compressor.

4. Is there a way to control the exit temperature of the air in a compressor?

Yes, there are several ways to control the exit temperature of the air in a compressor. These include adjusting the inlet temperature and pressure of the air, using intercoolers or aftercoolers to reduce the temperature between stages of compression, and implementing variable speed drives to adjust the speed of the compressor.

5. Why is it important to know the exit temperature of the air in a compressor?

The exit temperature of the air in a compressor is important to know because it can affect the overall efficiency and performance of the compressor. If the exit temperature is too high, it can lead to increased wear and tear on the compressor components, reduced efficiency, and potential damage to downstream equipment. By accurately calculating and monitoring the exit temperature, proper adjustments can be made to ensure optimal performance and prevent potential issues.

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