Twoideal Carnot engines opeate 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 the temperature of the sink of first engine which isi 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?

Twoideal Carnot engines opeate in cascade (all heat given up by one en

1.	Twoideal Carnot engines opeate 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 the temperature of the sink of first engine which isi 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?
Answer» `(2T_(1)T_(2))/(T_(1) + T_(2))` `(T_(1) + T_(2))/(2)` 0 `SQRT(T_(1)T_(2))` Solution :Suppose `Q_(H)=` Heat supplied to first engine `Q_(L)`= Heat extracted from first engine `Q._(L)`= Heat extracted from `2^(nd)` engine WORK done by first engine= work done by SECOND engine `Q_(H)- Q_(L) = Q_(L)- Q._(L)` `:. Q_(H)+ Q._(L) = 2Q_(L)` but `Q_(L) prop T and Q._(L) prop T_(2) "ALSO" Q_(H) prop T_(1)` `:. T_(1) + T_(2) = 2T` `:. T= (T_(1) +T_(2))/(2)`