Question

Consider a piston cylinder with a set of stops as illustrated in Figure Question 4 filled with CO2. Initially, the pressure, temperature and volume of the CO2 is 128 kPa, 135°C and 0.038 m', respectively. The piston cylinder then undergoes the polytropic expansion until the piston head reaches the set of stops. At this position, the pressure and temperature of the CO2 is 87 kPa and 68°C, respectively. The heat is then added to the CO2 until the temperature reaches 103°C. The piston cylinder is then compressed adiabatically to the pressure of 112 kPa. Finally, the piston moves back to the initial state isothermally. Determine the net works for these processes by taking specific heat at room temperature. Illustrate the processes in the P-v diagram. CO2 Piston Figure Question 4

Answer 1

# 3 2 V 2-3: 1-2:- Polytropic expansion Constant volume heat addition 3-4:- Reversible adiabatic compression 4-1:- Iso thermal Compression. Given, P = 128kpa; Ti = 135°C = 408k; % = 0.038 m3 ; P = 87 kpa ; T2 = 68°C =341k; 3 = 103°c = 376k ; P4 = 112 kpa For Polytropic process (1-2). Pe - (JM 2) So, Polytropic index (n) = 1.868 work Wiz R (T, -T2) Pi 87 128 341 408 for Co, gas, R = 8-314 44 = 0.1889 kJ/kg-k. so, Wiz 0.1889* (408-341). 1.868-1 14.585 KJ/kg

Taking co, as ideal Gas. Then, P. Y = MRT => 128x102 * 0.038 mx 0.1889 x 103 x 408. or mass of co, (m) = 0.063 kg For process 2-3 3 Tz . P3 P2 P3 376 341 87. So, P₂ = 95-93 kpa SP dv = o[volume is constant] W23 For process 3-4. r-1 r Py P₃ Т. For Con gas, r = 1.28 so, 0.28 1-28 (112 95.93 - Ty 1.376 - or, Ty 388.96 K W34 0-1889 *( 376-388.96) R (T3 - T4 (n-1) or Way = (1.28-1) -8.74 kJ /kg

[T = Tu = 408k for process 4-1 4-1 PK Wys RT; In (14) -0.1889*408* ln (1 2 of 128 =-10.29 kJ/kg So Net work transfer =m/Wht W₂ z t Wzy + Wyl m[ure 0.063[14.585+0 -8.74-10-29 -0.28 KJ or, Net Work = 280.035 J (Ans).

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