Two Carnot engines $A$ and $B$ are operated in succession. The first one, $A$ receives heat from a source at ${T_1} = 800K$ and rejects to sink at ${T_2}K.$. The second engine $B$ receives heat rejected by the first engine and rejects to another sink at ${T_3} = 300K.$ If the work outputs of two engines are equal, then the value of ${T_2}$ is .... $K$
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