Realistic thermal heat engine model and its generalized efficiency

We identify a realistic model of thermal heat engines and obtain the generalized efficiency, $\eta= 1- \left(\frac{T_c}{T_h}\right)^{1/\delta}$, where $\delta=1+\frac{1}{\gamma}$ and $\gamma$ is the ratio of thermal heat capacities of working substance at two thermal stages of the hot heat reservoir temperature, $T_h$ and the cold heat reservoir temperature, $T_c$. We find that the observed efficiency of practical heat engines satisfy the above generalized efficiency with $1/\delta=0.35594$ $\pm$ $0.07$. The Curzon-Ahlborn efficiency, $\eta_{CA}=1-\left(\frac{T_c}{T_h}\right)^{1/2}$ is obtained for the symmetric case, $\gamma=1$. The generalized efficiency approaches the Carnot efficiency, $\eta_C=1-\frac{T_c}{T_h}$, in the asymmetric limit, $\gamma \to \infty$.