Explain why the Carnot cycle overestimates the thermal efficiency achievable from an engine producing power output. Discuss why external irreversibility reduces the effective temperature ratio of an endoreversible engine.

Show that the thermal efficiency at maximum power output of an endoreversible engine executing an Otto cycle is

\[\eta_{\mathrm{th}}=1-\left(\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}}\right)^{1 / 2}\]

where \(T_{\mathrm{H}}=\) maximum temperature of the cycle and \(T_{\mathrm{C}}=\) minimum temperature of the cycle.