The Carnot engine is defined in a way that makes calculation of its properties easy. The main expansion and compression paths are isotherms. The paths connecting the isotherms are adiabats. On an isotherm there is no temperature change, so that for an ideal gas, all the heat input is converted to work. On an adiabat, no heat flows, making the change in internal energy easy to calculate from the work done.
Calculations indicate that ratio of heat flows on the high and low temperature isotherms is equal to the ratio of the temperatures. As a result, the efficiency of the Carnot engine is given by
{efficiency} = 1-(T low)/(T high)
where an efficiency of 1 indicates perfect conversion of heat into work during a complete cycle of the engine.
In a Carnot engine, the entropy of the universe remains constant while the engine does its work. No engine can do better than that.