The rate of entropy generation can be derived from: $\dot{S}_{gen}=\dfrac{dS_{cv}}{dt}+\dfrac{dS_{surr}}{dt}$ By definition, for a [[Steady State|steady state]] process $\dfrac{dS_{cv}}{dt}=0$. All that remains is to define entropy generation from the surroundings, $\dfrac{dS_{surr}}{dt}=0$. $\dfrac{dS_{surr}}{dt}=\sum\dot{m}_es_e−\sum\dot{m}_is_i-\dfrac{\dot{Q}_{cv}}{T_{surr}}$