The Carnot subcritical cycle is a theoretical thermodynamic cycle comprised of two isothermal and two adiabatic processes. It’s processes consist of adiabatic compression, isothermal expansion, adiabatic expansion and isothermal compression in a repeating cycle. Thermal fluids are the medium in which energy flows through the system. Water is a common thermal fluid and since the cycle is subcritical, the processes that will be analysed will act on water before it reaches its critical state.

The main principle behind a Carnot Cycle is that no thermodynamic system can be more efficient than one which is isentropic. The theory behind an isentropic cycle, is that in magnitude, it is reversibly equivalent to its intended cycle. For a system to be considered reversible, entropy cannot exist throughout any point in the cycle, however entropy is inevitable under any realistic conditions.

Figure 1: A Carnot Cycle [2]

Figure 1 consists of four basic components, being a pump, a boiler, a turbine, and a condenser. Isothermal expansion occurs throughout state 1 while the fluid is leaving the condenser and entering the pump. The fluid expands under constant temperature, resulting in a decrease in pressure and a loss of heat.  Adiabatic compression increases pressure and temperature without any gain or loss of heat throughout state 2. Due to idealized conditions, it can be assumed that the entropy remains constant throughout states 1 and 2. Isothermal compression occurs as the the liquid moves from the boiler to the turbine in state 3. While the temperature remains constant, the pressure increase results in a resulting increase in internal energy. Entropy does change between states 2 and 3, however the pressure remains constant. Adiabatic expansion returns the liquid back to the start of the cycle as the fluid leaves the pump and enters the condenser as seen in state 4. No heat exchange occurs, causing the temperature to change as a result of the pressure change. The changes in entropy with respect to temperature can be seen graphically in Figure 2. Changes in enthalpy with respect to pressure can be seen graphically in Figure 3.

Figure 2: A carnot cycle represented graphically through a temperature vs. entropy plot[3]

Figure 3: A carnot cycle represented graphically through a pressure vs. enthalpy plot [4]

Table 1 shows the results from hand calculations using the mentioned example conditions. Water property tables that have been empirically derived are used to attain the values for specific enthalpy and specific enthalpy. The nodes in the table refer to the nodes shown above in Figure 1.

Table 1: Results from hand calculations for specific enthalpy and specific entropy.

The first law of thermodynamics states that energy can neither be created nor destroyed. For our example, this means that the energy of the water can change form, but any change in the total energy of the water must have been affected by its surroundings. The water can change temperature, pressure, and quality but only work experienced by the water and heat transfer will affect its total energy.

After determining the specific enthalpy at each of the nodes, an energy balance can be calculated at each of the devices to find the rate of energy intake/output at that device. This calculation is shown for each device in Figure 1, simply by multiplying the mass flow rate by the change in enthalpy across the device. This results in values for the power output of the turbine, the rate of heat transfer into the boiler, the rate of heat transfer out of the condenser and the power required by the pump. The second law of thermodynamics holds true for these processes since the entropy does not decrease through the pump and the turbine.

Figure 4: Hand calculations for energy balance and thermal efficiency.

With the rate of energy transfer known at every device in the cycle, the thermal efficiency can be calculated as shown in Figure 4. Since this is the Carnot cycle for the given conditions, the efficiency calculated of 38% is the ideal maximum efficiency. By altering the high and low temperature of the cycle, the efficiency will be altered. Finding the optimal temperature conditions is critical to finding the most efficient cycle.