Question

b) Figure Q1(b) shows a P-v diagram consists of isentropic, polytropic, and isothermal compression processes between the same pressure limits. Based on the figure, distinguish the work input to the compressor for all the three processes. (6 marks) PA -Isentropic (n = k) -Polytropic (1 <n<k) Isothermal (n = 1) Pi 1 V Figure Q1(b)

Answer 1

Hello student I am providing you figure of compressor operation on p-v diagram and then deriving general formula.

Discharge Creciever) - Piston Cylinder arrangement Disc orplate D.V type valve S.V Suction (Atmosphere) Discharge 2 P2 3 - - → - P compression k prn=c Suction P st 1 V2 VI

work done * Work input required without dealance Volume :- /per by cycle is given by area (1-2-3-4-1) by suction, during (4-1), P,. (Vi-o) =Pi. Vi work done air -> Ws = Work done on ail during compression, (1-2), Wc = P.VI - P2 V2 (n-1) - (P2.12 -PIVI) (4-1)

wa P2. (0-V2) = -P2 V2 [P2 V2 - P.VI + P2.V2 - P. Vi (n-D 1 Weyle = - [Bv2 - P PIV) { 9:[2+ ht] - CP2 V2 - PVD. (1+ 2 w/ cycle P2 V2 - PIVI W/eyele So -ve, s taking only the magnitude. As compressor work is always wo/cycle (P2V2-pivi) и n-1 P, V, - 1 и n-1 W/cycle P2 PI Vz Vi for process 1-2 Pivin= Pz kn 11/n Vi 1-1/n V2 Pz Pi Ten) [ () M-11 P. VI. W/eyne (4) w/eyele -). .PI.VI. (P2 ] 1 2 1 2 1 n-1 Pi Pi-kPa, Vi-m3/jele (kJ/cycle)

So work per cylce for compressor is derived above now put value of n as per process.

If process is isothermal then put n=1

If process is adiabatic then put n= 1.4 that is k

If process is polytropic then put n = 1 to 1.4

Above all process is reversible.

So put value of n you will get your required formula for all those three mentioned curve.

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