# Conservation of energy during compression?

1. Aug 21, 2010

### Mike_In_Plano

Hello,

I have a quick question regarding what goes on in air compressors.

When air is compressed, I understand that we're doing a couple of things:
1. Squeezing a mass rate of air from one pressure to another - which takes work
2. Imparting heat to the gas stream - again part of doing the work.

My question is, what equations would you use to determine how much of the work went towards elevating the pressure and how much was expended as waste heat when compressing air and then cooling it back to its original temperature?

Thanks,

Mike in Plano

2. Aug 22, 2010

### AJ Bentley

That's an entire branch of physics.
Thermodynamics.

3. Aug 22, 2010

### Bob S

4. Aug 22, 2010

### Mike_In_Plano

So, I'm guessing that the best way to approach this problem is to determine the work done when performing the adiabatic compression and subtract the energy lost during the isobaric cooling?

5. Aug 22, 2010

### hydrogen1

This is a problem that can be solved best with a basic energy balance on an open system(your compressor).

rate of energy out - rate of energy in = W + Q
$$\dot{m}$$($$\Delta$$H +$$\Delta$$$$u^{2}$$/2+g$$\Delta$$h)= W+Q

W=work rate(power)
Q=heat
H=enthalpy at some T&P
u=average fluid velocity(could be turbulent could be laminar)
h=height
$$\dot{m}$$=mass flowrate

more than likely the potential and kinetic terms are negligible

to get a strong estimate of the work rate of the compressor:
W = $$\dot{m}$$$$\Delta$$H

6. Aug 23, 2010

### Mike_In_Plano

Wow,

Thanks Hydrogen.

So, I just need to get an idea of my mass flow rate from the CFM at STP and gas density. Then, I can pull get the enthalpy for the start and end conditions from my gas tables. Use the delta for my enthalpy to compute the rate of work done from one end to the other.

As for the efficiency of the system, I'm thinking the overall work done is the resulting differential energy (from the delta-h)m divided by the work done during the adiabatic compression?

7. Aug 25, 2010

### hydrogen1

(delta H)/(delta H)s= the efficiency where subscript s means the delta H for the isoentropic process this is a definition of efficiency.

8. Aug 25, 2010

### Mike_In_Plano

Thanks Hydrogen,