Two Carnot engines $A$ and $B$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $T$. The second engine $B$ receives the heat at temperature $T$ and rejects to its sink at temperature $T_2$. For what value of $T$ are the efficiencies of the two engines equal?

• A
  $\frac{T_1 + T_2}{2}$
• B
  $\frac{T_1 - T_2}{2}$
• C
  $T_1 T_2$
• D
  $\sqrt{T_1 T_2}$