Realistic thermal heat engine model and its generalized efficiency

We identify a realistic model of thermal heat engines and obtain the generalized efficiency, $\eta =1-{\left(\frac{T_c}{T_h}\right)}^{1\mathrm{/}\delta }$, 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 $1\mathrm{/}\delta =0.35594$ $\pm$ $0.07$. The Curzon-Ahlborn efficiency, ${\eta }_{CA}=1-{\left(\frac{T_c}{T_h}\right)}^{1\mathrm{/}2}$ 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, $\gamma \to \mathrm{\infty }$.