How Do Carnot's Efficiency Formulas for Heat Engines Align?

[Tulio Cesar]

My question is: according to Carnot cycle, the maximum efficiency of a heat engine is given by 1 - T2/T1, where T2 is the temperature of the cold source and T1 the temperature of the hot source. So, accordingly, as higher T2 is for a same T1, lowest is the efficiency of the engine. But, the other formula for efficiency (1 - Q2/Q1), gets me confuse because as bigger temperature is, minus heat is exchanged with the cold source, and as lower temperature is, more heat is exchanged with de hot source. I don't know if I missed any point but these two formulas seem contradictory for me.

 

[lychette]

The analysis of heat engines centres around the expansion of gases. It is possible to show that the work (energy) involved in compressing or expanding gases is give by P x V ,( area under P~ V graph or ∫P.dV ).
From the gas laws it is possible to show that P x V ∝ T.
This means that heat energy is proportional to Absolute temp (T) and therefore the expressions Q in your equation can be replaced by T