# Thermodynamics question - does power required mean same as power output?

1. Aug 3, 2011

How to find power required for adiabatic compressor?
Problem - Air enters an adiabatic compressor at 20 C and 1bar. The volumetric flow rate of air is 1 m3/s and it exits at 200 C. Determine the power required if the isentropic efficiency of the compressor is 80%.

Density of water = 1000 kg/m^3
Mass flow rate m = 1 m^3/s * 1000 kg/m^3 = 1000 kg/s
I know that power output is calculated by
m Cp (T2 - T1)

But what is meant by power required? Is it same as power output or is it power input?
If it is power output, then we can calculate it using m Cp (T2 - T1)
If it is power input, then can we use work required = power output/(isentropic efficiency) ?

The problem involves a range of temperatures. I have to use the values of density, Cp and any other constants needed at what temperature? Initial? Final? Average?

2. Aug 3, 2011

### NewtonianAlch

I guess it means the power required to allow that 80% efficiency therefore it would be an input, if something is requiring power, it's awaiting an input.

3. Aug 3, 2011

### Andrew Mason

First find the power required to compress 1 m^3 of air every second. Hint: you have to determine the final compressed volume of that 1 m^3 of air. You are given its final temperature. What is the relationship between temperature and volume during an adiabatic compression? What is the work done?

Second, determine how much input power is required at 80% efficiency (ie only 80% of the input energy does work in compressing the air.

AM

4. Aug 4, 2011

### SteamKing

Staff Emeritus
Hint: The density of water (1000 kg/m^3) is not the same as the density of the air moving through the compressor.)