$(10$pts$)$ Consider the heat engine operating at steady state between the two thermal

reservoirs shown at the right while producing a net power output of $700$ kW $.$ If $1000$

kW of heat $(Q_H^{})$ is transferred to the heat engine from a thermal reservoir at a

temperature of $T_H=900K,$ and heat is rejected to a thermal reservoir at a temperature

of $T_L=300K,$ is this heat engine possible?