BC is an adiabatic process, and Poisson formula can be used directly. I believe that there must be no thermal change in the textbook, Q=0, and doing work equals negative internal energy change;
Isothermal heat release of CA Q Ca = n * CP * (TC-TA) = 5/2 * NR (TC-TA) = 5/2 * p1* (V2-V1) = 5/2 * (2 (3/5)-6544.
The efficiency is w /Q =1-q amplification/q absorption =1-q ca/q ab =1-5/3 * (2 (3/5)-1).