# Homework Help: Thermodynamics - Vapour Power Plants

1. May 3, 2010

### geordieman101

1. The problem statement, all variables and given/known data
A compressor takes in 4 kg/s of air at atmospheric pressure and temperature, 1 bar and 25 degrees C. Air leaves the compressor at 4 bars and 200 degreesC. Calculate the power input to the compressor and its isentropic efficiency. For air Cp=1.005 and Cv=0.718 kJ/kg K

Answers: (703.5 kW, 0.83)

2. Relevant equations

(h2s - h1)/(h2-h1)

3. The attempt at a solution
I have already calculated the power input by using mass flow rate x Cp x delta T, however I am unable to find the isentropic efficiency. My attempt so far has been to divide Power input by mass flow rate to obtain h2-h1. The h2-h1 value i have obtained is 175.9kJ. I need help in finding h2s-h1.

I am doing this questions as exam preparation (this has nothing to do with coursework/homework) so maximum help would be very helpful.

Thanks

2. May 5, 2010

### RTW69

Find a table of ideal gas properties for air that list T, h and Pr. Pr is the relative pressure for air when S2-S1=0 (constant entropy). Find h1, h2 and Pr1 from the table, h2s is tricky.

For the special case of air modeled as an ideal gas and S2-S1=0 this relation holds true:

P2/P1=Pr2/Pr1 solve for Pr2. Look up Pr2 in table and note corresponding h2s of about 443 Kj/Kg

From Fundamentals of Engineering Thermo. Moran and Shapiro edition 4, P. 276