Could someone help me study this cyclic process of an ideal gas?

[Chestermiller]

I have a follow-up question (also to @Chestermiller):

W_1-2 has to be the same as -Q_h so that ΔU becomes zero for a complete cycle.

I have a follow-up question (also to @Chestermiller):

W_1-2 has to be the same as -Q_h so that ΔU becomes zero for a complete cycle.

If, however, I insist on calculating W_1-2 as P_ext ΔV I'm a bit stuck.
With P_ext equal to P₂, the internal pressure in state 2 (which seemed the obvious choice to me), I get only about half of -890 J.
Surely P_ext can't be higher than P₂.

If, however, I insist on calculating W_1-2 as P_ext ΔV I'm a bit stuck.
With P_ext equal to P₂, the internal pressure in state 2 (which seemed the obvious choice to me), I get only about half of -890 J.
Surely P_ext can't be higher than P₂.

Unless you know $P_{ext}$ explicitly for an irreversible expansion or compression, you can not determine the work (without solving the internal Navier Stokes equation, the continuity equation, and the differential thermal energy balances equation simultaneously).