Question 2.7: A three-process cycle operating with nitrogen as working sub......
A three-process cycle operating with nitrogen as working substance has constant temperature compression at 34°C with initial pressure 100 kPa. Then the gas undergoes constant volume heating and then a polytropic expansion with 1.35 as index of expansion. The isothermal work requires 67 kJ/kg of work. Determine the state coordinates and net work transfer. (AU, 2013)
For state 1:
Characteristic gas constant R of Nitrogen, R_N = \frac{R}{28} = \frac{8.314}{28} = 0.297\frac{kJ}{kg K}
V_1 = \frac{R_NT_1}{p_1} = \frac{0.297 \times (273 + 34)}{100} = 0.912 m^3
For state 2:
W_{12} = p_1V_1 \log \frac{V_2}{V_1}
– 67 = 100 \times 0.912 \log \frac{V_2}{0.912} \longrightarrow V_2 = 0.4375 m^3
\frac{p_2V_2}{T_2} = \frac{p_1V_1}{T_1} \longrightarrow p_2 = \frac{p_1V_1}{V_2} = 208.46 kPa ; T_2=T_1
For state 3:
V_3 = V_2 = 0.4375 m^3
p_3V^{1.35}_3 = p_1V^{1.35}_1 \longrightarrow p_3 = 269.65 kPa
\frac{p_1V_1}{T_1} = \frac{p_3V_3}{T_3} \longrightarrow T_3 = \frac{p_3V_3}{p_1V_1} T_1 = 397 K