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 will distinguish their work required in each of these three process but before that I will show you on p-v diagram and giving you general formula for work input per cylce for compressor.

Discharge P2 3 2 P compression 1 k prn=c Suction > 4 P 1 V2 Vi

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

Wd P2. (0-2) = -P2 V2 [P2 V2 - P.VI + P2. V2 - P. Vi (n-D Weyele -- [13V2- Pivool 0,[1+] - CP2 V2 - PVD. (1+ 2 w/ cycle P2 V2 - Pivi W/cycle AS -ve, so taking only the magnitude. compressor work is always wo/cycle (P2V2-pivi и n-1 PIVI -1 W/eyele (1) [ P2 Pi Vz Vi for process 1-2 Pivin = P2 kn 1/n 1-1/ V2 Pi P2 P2 Pi VI P. VI. (3) -1 w/eyde (m) w/eyele -). и n-1 .P.VI. in-1 P2 Pi 1 1 1 1 PickPa, Vi- mljele -1 (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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Thank you