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Three Carnot engines operate in series between a heat source at a temperature $T_1$ and a heat sink at temperature $T_4$ (see figure). There are two other reservoirs at temperature $T_2$ and $T_3$, as shown, with $T_1 > T_2 > T_3 > T_4$. The three engines are equally efficient if

• A
  ${T_2} = {\left( {{T_1}{T_4}} \right)^{1/2}};\,{T_3} = {\left( {T_1^2{T_4}} \right)^{1/3}}$
• ✓
  ${T_2} = {\left( {T_1^2{T_4}} \right)^{1/3}};\,{T_3} = {\left( {{T_1}T_4^2} \right)^{1/3}}$
• C
  ${T_2} = {\left( {{T_1}T_4^2} \right)^{1/3}};\,{T_3} = {\left( {T_1^2{T_4}} \right)^{1/3}}$
• D
  ${T_2} = {\left( {T_1^3{T_4}} \right)^{1/4}};\,{T_3} = {\left( {{T_1}T_4^3} \right)^{1/4}}$