By integrating all the terms for [[Entropy Generation Rate|entropy generation]] as a rate we can calculate the entropy generation for a transient process. $\int_{t_1}^{t_2}\dfrac{dS_{cv}}{dt}dt=(m_2s_2−m_1s_1)_{cv}$ $\int_{t_1}^{t_2}\left(\sum\dot{m}_es_e−\sum\dot{m}_is_i\right)dt=\sum m_es_e−\sum m_is_i$ $\int_{t_1}^{t_2}\dfrac{\dot{Q}_{cv}}{T_{surr}}dt=\dfrac{Q_{1to2}}{T_{surr}}$ Overall the entropy generation for a transient process will be: $S_{1\to2}=(m_2s_2−m_1s_1)_{cv}+\sum m_es_e−\sum m_is_i−\dfrac{Q_{1\to2}}{T_{surr}}$