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Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperatures T2 and T3, as shown with T1 > T2 > T3 > T4. The three engines are equally efficient if

A. \({T_2} = {\left( {T_1^3{T_4}} \right)^{1/4}};{T_3} = {\left( {{T_1}T_4^3} \right)^{\frac{1}{4}}}\)
B. \({T_2} = {\left( {T_1^2{T_4}} \right)^{1/3}};{T_3} = {\left( {{T_1}T_4^2} \right)^{\frac{1}{3}}}\)
C. \({T_2} = {\left( {{T_1}{T_4}} \right)^{1/2}};{T_3} = {\left( {T_1^2{T_4}} \right)^{\frac{1}{3}}}\)
D. \({T_2} = {\left( {{T_1}T_4^2} \right)^{1/3}};{T_3} = {\left( {T_1^2{T_4}} \right)^{\frac{1}{3}}}\)
Answer» C. \({T_2} = {\left( {{T_1}{T_4}} \right)^{1/2}};{T_3} = {\left( {T_1^2{T_4}} \right)^{\frac{1}{3}}}\)


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