Question

One kg of ideal gas at pressure at 1bar, volume 0.3m 3 , and temperature 25 degree C. The gas compressed polytropicaly to half its initial volume the pressure become 10 bar, then it’s expanded adiabatically to its original volume. If you know that =1.41 and Cp= 1.001kJ/kg K. Draw the processes on P-V ; T-S diagrams, what is the third process that retained the gas to its initial state?

Determine:
I) The gas properties at each point.

Answer 1

The ideal gas undergoes polytropic compression, adiabatic expansion, and finally isobaric cooling to return to its initial state. At each process, the gas properties change, which can be plotted on P-V and T-S diagrams.

Step-by-step explanation:

The ideal gas mentioned in the question undergoes three processes. Initially, it is compressed polytropically to half of its volume, with the pressure rising to 10 bar. Then it is expanded adiabatically back to the original volume. To complete the cycle and return the gas to its initial state, it must undergo an isobaric cooling process.

To characterize the gas properties at each point:

• Initial state (1): P1 = 1 bar, V1 = 0.3 m3, T1 = 25 °C
• After polytropic compression (2): P2 = 10 bar, V2 = 0.15 m3
• After adiabatic expansion (3): P3 is such that P3*V3κ = P2*V2κ, V3 = V1 = 0.3 m3
• Finally, to return to initial state (4): P4 = P1, V4 = V1, T4 = T1

The P-V and T-S diagrams for these processes would show the changes in pressure, volume, temperature, and entropy for each step. The third process to return the gas to its initial state would be the isobaric cooling.