Carnot vs Rankine cycle

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In brief, the Carnot heat engine is theoretical. It was conceived to deliver maximum efficiency to become a benchmark for efficiency that a heat engine can produce. Rankine cycle is a modified version of the Carnot cycle that addresses some of the weak links of the Carnot cycle and makes it practical to use on the ground. The Rankine cycle is extensively used in power generation.

The Carnot cycle is a constant internal energy cycle at constant temperature while the Rankine cycle is a constant enthalpy cycle at constant pressure. At constant temperature, the Carnot cycle has infinite heat capacity. ?

In the Carnot cycle, the working fluid moves at a constant temperature through its four arms and reaches the same pressure and temperature at the end of the cycle from the point the cycle starts its journey. ?Thus the net internal energy change, dU = 0. This means from the 1st law of thermodynamics, dU = delta Q - delta W = 0. In other words, delta Q = delta W remains throughout the cycle. This makes the Carnot cycle a reversible cycle with Q = W and no entropy generation. ?However, this makes the Carnot cycle an infinitesimally slow cycle. ?

The Carnot cycle has one isothermal expansion hot reservoir which adds internal energy to saturated water by expanding and breaking its H bonds releasing the huge potential energy held in intermolecular bonds and converting saturated water to saturated steam at constant temperature.

The next arm of the Carnot cycle is an adiabatic expansion, ( - W work) of steam that pulls internal energy to spin the turbine and cools down the steam to saturated steam temperature. The next is an isothermal compression arm ( + W work) that adds back the internal energy consumed in stage 2 by compressing the fluid from stage 2 at constant temperature by reducing volume or increasing the density of water making water release of latent heat of condensation. This stage is called heat sink.

The fourth arm is adiabatic compression. This arm's (pump) job is to raise the internal energy to the same level that is stage 1 from where the working fluid(steam) starts the journey and completes the cycle. Rankine realized isothermal heat addition and heat rejection is impossible for a practical heat engine on the ground.

Rankine modified the Carnot cycle by replacing the two isothermal arms by constant pressure arms and focussed on the total energy, enthalpy at constant pressure, dH = dU + PdV. This opened up the option to use superheated steam in the Rankine cycle.

Essentially, Rankine tracked the total energy as it moved round the cycle while Carnot tracked the internal energy. The rankine cycle has also two adiabatic arms like the Carnot cycle. Their jobs are similar. In stage 2 the adiabatic arm extracts enthalpy to run the turbine and in stage 4 the adiabatic arm adds back the enthalpy. In the Rankine cycle, the heat reservoirs are not reversible. They do generate entropy as the working fluid expands and gets compressed.