Question

A sketch of set of four processes involved in a closed thermodynamic system is shown in the adjoining pressure- volume diagram. Isothermal expansion brings 220 grams of a fluid from 415 kPa to a final pressure of 115 kPa and specific volume of 120 litres/kilogram. A reversible cooling process takes place at constant pressure with a work done of 525 Joules and then followed by a constant volume until the pressure of the fluid becomes 62 kPa. A Polytropic compression process brings the fluid back to its original conditions. Determine: a) The total volume at state point 2 b) The total volume at state point 1 c) Work done for the isothermal expansion process 1-2 d) Total volume at state point 3 e) Work done for the isochoric expansion process 3-4 f) Polytropic index for the Polytropic process 4-1 8) Work done for the Polytropic process 4-1 h) The net-work done in the cycle 1-2-3-4-1. QUESTION 6

Answer 1

Solution PA M= 220grams = 0.2 Kg P = 415kpa P = 115K Pa = P3 C W2-3 = 525 Joules 2. 3 18 = 1/2 = 120 litres Tag 2 m. 4 PA 62 KP a 2-3 1 - 2 + Isothermal Expansion constant pressure Cooling 3-4 constant Volume process 4-1 + polytropic Compression la Total Volume @ State. q. Sp. Volume, V = Volume mass 1/2 = V2 Va = m V2 1m3 = 1ooolitee m Vo = 0.2 x 120 = 0.024 m3 1000 Total Volume @ State 1. PNI P2 V2 T T2 1-2 Isothermal Expansion Ti = T2 Pivi = P2 V2 415% Vi= 115 X 0.024 Vi = 0.0066m3

Workdone For Isothermal process Wi-2= Piviln Piviln (V) = 415x0.0066 in 0.024 0.00 66 Wi-2 = 3.53 KJ = 3536 Joules a Total Volume @ State 3 W2 - 3 = P2 (V3 - V2) 0.525 = 115 ( V3 – 0.024) V3 = 0.0285 m 3 = V4 e Woskdone Fos Isochoric expansion 3-4 W3-4 = 0 ( Since No displacement) V₂ =V3

Woskdone in polytropic process 4-1 Wq-1=PqV4 - P.Vi n-1. n / 4 log inlog $ polytropic Index foe procese 4-1 By pressure Volume - Relation. PA Р. VA log IPA =nlog VI 1/4 62 0.0066 415 O. 0285 n=1.30 Wosk done in poly tow pic porocess 4-1 W4-) - PAVA - Pili n- = (62*0,0285) - (415 +0.0066) 1-30- Wa-1= -3.20KJ W14-1 = - 3200 Joules b Net Wloskdone Cycle 1-2-3-4-1 Winet = hli- at W2-3 + W3-4 t WA-1 = 3536 + 525 t 0 - 3200 Whet = 861 Joules