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Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures \( T_{1} \) and \( T_{2} \). The temperature of the hot reservoir of the first engine is \( T_{1} \) and the temperature of the cold reservoir of the second engine is \( T_{2} . T \) is temperature of the sink of first engine which is also the source for the second engine. How is \( T \) related to \( T_{1} \) and \( T_{2} \), if both the engines perform equal amount of work?
(a) \( T=0 \)
(b) \( T=\frac{2 T_{1} T_{2}}{T_{1}+T_{2}} \)
(c) \( T=\sqrt{T_{1} T_{2}} \)
(d) \( T=\frac{T_{1}+T_{2}}{2} \)
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