The efficiency of Rankine cycle is lower than that of corresponding Carnot cycle because

Concept:

Note that the Rankine cycle has a lower efficiency compared to the corresponding Carnot cycle 2’-3-4-1’ with the same maximum and minimum temperatures. The reason is that the average temperature at which heat is added in the Rankine cycle lies between T2 and T2' and is thus less than the constant temperature T2' at which heat is added to the Carnot cycle.

It is very difficult to build a pump that will handle a mixture of liquid and vapour at state 1' (refer T-s diagram; Carnot Vapor Cycle) and deliver saturated liquid at state 2’.

It is much easier to completely condense the vapour and handle only liquid in the pump (Rankine Cycle)

Additional Information

In the Carnot cycle, the compression is wet compression so the pump work requirement is more compare to the Rankine cycle where the pump compresses only the saturated liquid. Thus the specific work output for the Rankine cycle is more than the Carnot cycle for the same maximum and minimum temperature.

Also, the work ratio is defined as the ratio of net-work to the work done in the turbine.

\(r_w=\frac{W_{net}}{W_T}=\frac{W_T-W_C}{W_T}\)

Thus the work ratio is low for the Carnot Cycle.