What is the Outlet Temperature of a Compressed Air Flow?

[FreelandME]

Homework Statement

Air enters a compressor at 100kPa and 20 oC in steady flow rate . Air is compressed to 1 Mpa. The heat loss is 10% of the power of the compressor . Air enters with speed of 50m/s in a surface of 0,009 m² and leaves with speed 120 m/s from a surface of 0,0005 m².

Find the output temperature .

Homework Equations

[/B]
Q12 - W 12 = m [ h₂ - h₁ + (V₂- V₁)/2+ g (z₂-z₁)] (1)
m=pAV (mass flow rate)

The Attempt at a Solution

confused how i should use the data to find temperature (i'm pretty sure thermodynamic table of properties of air can be used )

 

[Chestermiller]

What is the density of the air coming in. What is the mass flow rate of the air through the compressor?

Chet

 

[FreelandME]

There is no information about either , the only thing we can use are thermodynamic tables but i really have no idea how to use them in the current problem

 

[Chestermiller]

There is no information about either , the only thing we can use are thermodynamic tables but i really have no idea how to use them in the current problem

If you know that temperature and pressure of a gas, then the density of the gas is determined. At the inlet conditions, the ideal gas law should provide a very accurate estimate of the air density. If you are not happy with the accuracy of that, then you can use your thermodynamic tables. (You are aware that density is the reciprocal of specific volume, correct?) So, what is the density of the air at the inlet conditions.

Chet

 

[FreelandME]

So i find from the ideal gas law that the density of air is ~1.28 kg/m³ so with that i find the mass flow which is m=0.576 kg/s , but how can i find the temperature in outlet in order to find the h2 and finish the problem

 

[Chestermiller]

So i find from the ideal gas law that the density of air is ~1.28 kg/m³ so with that i find the mass flow which is m=0.576 kg/s , but how can i find the temperature in outlet in order to find the h2 and finish the problem

The mass flow rate is constant, and you know the final volumetric flow rate, so you know the final density. If you know the final density and final pressure, you know the final temperature.

Chet

 

[FreelandME]

So the
m=pA₂V₂ => p=9.6 kg/m³
from ideal gas law
p=MP/RT
we get T2~367.78 K

is that correct or do i miss something ?

 

[Chestermiller]

So the
m=pA₂V₂ => p=9.6 kg/m³
from ideal gas law
p=MP/RT
we get T2~367.78 K

is that correct or do i miss something ?

Yes, if you did the arithmetic correctly.

Chet

 

[FreelandME]

then i use the T2 and T1 to find enthalpies from ideal gas proprties of air table and solve
Q12 - W 12 = m [ h2 - h1 + (V2- V1)/2+ g (z2-z1)] (1)
where z2-z1=0
m=0.576 kg/s
Q=0.1 W
and h2-h1 the enthalpies from the table?

Is that correct right?

 

[Chestermiller]

I thought that all the problem asked for was the outlet temperature, which you already have.

Chet