In the arcjet illustrated in the diagram, arc length L is 1 cm and the voltage across it i...

In the arcjet illustrated in the diagram, arc length L is 1 cm and the voltage across it is 100 V. The voltage drop across the anode layer, which is Δa = 1 mm thick, is 22 V. The voltage difference across the cathode layer, which is Δc = 3 mm, is 37 V.

Assuming half the electrical heating energy of the cathode layer goes into the cathode and that all of the heating energy of the anode layer goes into the anode, estimate the fractional loss to the walls of the energy added to the flow and the total power input. The arc current is 25,000 A.

The working fluid is helium, which enters the arcjet at 2.1 MPa and 300 K. Its flow rate is 44.64 g/s, and the polytropic expansion coefficient is estimated to be 1.37. The nozzle area ratio is 20:1.

Determine the specific impulse of the arcjet, assuming as a first approximation that nozzle heat transfer is negligible and that friction is important only downstream of the nozzle throat.